Mathematics Enhanced Scope And Sequence Algebra Ii Answers
Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 1188018: Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term to the (n+5) term.
Answer by greenestamps(9971)
You can put this solution on YOUR website! S(n) = a+ar+ar^2+...+ar^(n-1) S(n) = a(1+r+r^2+...+r^(n-1) We are given a=3/8, r=-2, and S(n) = -8191.875. Plug the numbers into the formula to determine n. We are to find the sum of the (n+1) term to the (n+5) term, or the sum of the 17th to 21st terms, which is S(21)-S(16). And then ANSWER: 270336
Question 1187892: What is the pattern for this sequence: 16, 8, 9, 12, 9, 16, 16, 9, 14
Answer by greenestamps(9971)
You can put this solution on YOUR website! It is impossible to know what the pattern is, or what the next number(s) are. Any subsequent numbers will make a valid sequence. There are an infinite number of "patterns" that will produce the given sequence; and they will produce different subsequent numbers. Without any more information about the given sequence, any problem like this is just a guessing game. Spend as much (or as little) time as you want looking for a logical pattern -- knowing that any pattern you find might not be "right".
Question 1187888: the 17 th term of sequence 3, 9, 27, 81, and so on.
Answer by ikleyn(42188)
Question 1187650: The seventh term of an arithmetic sequence is 25. Its first, third, and 21st
term form a geometric sequence. Find the first term and the common
difference of the sequence
Answer by greenestamps(9971)
You can put this solution on YOUR website! If the first term is a and the common difference is d, then 3rd term: a+2d The given information is [1] Working with [2] will give you an expression for d in terms of a; substituting the result into [1] will give you the answer. I'll get you started; the rest is straightforward. d=4a You can finish....
7th term: a+6d
21st term: a+20d (the 7th term is 25)
[2] (the 1st, 3rd, and 21st term form a geometric sequence)
Question 1187638: T3=24 T6=60
FIND THE COMMON DIFF AND THE FIRST TERM (a)
Answer by Theo(11773)
You can put this solution on YOUR website! you are given that A3 = 24 and A6 = 60. your common difference is 12. your first term is A1. A6 - A1 = 5 the common difference is 12. if you wish to use the formula to solve for this, do the followng. the formula is An = A1 + (n-1) * d this makes: subtract the first equation from the first to get: go to either one of the formulas and replace d with 12. do the same thing with A6 and you get A1 = 0 as well, as you should, since A1 is the same in both formulas.
without going through the formula, you can find the common difference in the following manner.
6 - 3 = 3
60 - 24 = 36
36/3 = 12
A3 - A1 = 2
24 - 2*12 = 24 - 24 = 0
A1 = 0
60 - 5*12 = 60 - 60 = 0
A1 = 0
your first term is 0.
24 = A1 + 2 * d
60 = A1 + 5 * d
36 = 3 * d
solve for d to get d = 12.
24 = A1 + 24
solve for A1 to get A1 = 0
Question 1187548: 76, 80, 88, 95, 100, 101
Answer by greenestamps(9971)
You can put this solution on YOUR website! (1) You didn't ask a question (2) Assuming that the question is to find the next number, or the next few numbers, the answer is that there is no one right answer. Any subsequent numbers in the sequence will form a valid sequence. On any problem like this, spend as much or as little time as you want trying to find a logical pattern that produces the given sequence of numbers -- knowing that any answer you find might not be right.
Question 1187380: If the 2nd and 5th term of a geometric progression are -6 48 respectively, find the sum of the 5th first four terms
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(42188)
You can put this solution on YOUR website! What is the meaning of this passage
. find the sum of the 5th first four terms.
in your post ?
Answer by Boreal(14475)
You can put this solution on YOUR website!
3 terms apart have a ratio of -8 in a geometric progression so r=-2. If second term is -6, first term is 3.
sum is a(1-r^n)/(1-r)
S= 3((1-(-2)^4)/(1-(-2))
=-45/3
=-15
the terms are 3, -6, 12, -24, 48
That is the first five terms, and the sum of the first four is -15
Question 1187317: Please help me find the 50th term in the arithmetic sequence.
5,9,13,17,...... Also, please explain it to me, thank you!
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(9971)
You can put this solution on YOUR website! Use the definition of an arithmetic sequence and do some simple calculations. The first term is 5. The 3rd term is the 1st term, plus 2 times the common difference: 5+2(4)=5+8=13
The second term, 9, is the first term, 5, plus the common difference; so the common difference is 4. Then...
The 4th term is the 1st term, plus 3 times the common difference: 5+3(4)=5+12=17
...
The 50th term is the 1st term, plus 49 times the common difference...
Answer by josgarithmetic(36644)
(Show Source): Question 1187260: It is a kind of sequence where every term after the first is obtained by multiplying a constant called common ratio. *
1 point
Harmonic Sequence
Fibonacci Sequence
Geometric Sequence
Arithmetic Sequence
Answer by ikleyn(42188)
Question 1187213: The sum of four numbers in an arithmetic progression is 98. The sum of their squares is 3006. Find the third number.
Answer by ikleyn(42188)
You can put this solution on YOUR website!
.
The sum of four numbers in an arithmetic progression is 98.
The sum of their squares is 3006. Find the third number.
~~~~~~~~~~~~~~~~~ Let
,
,
,
be four terms of the AP. Let "c" be the central point in the number line, exactly half way between the terms
and
. Let d be the HALF of the common difference of the progression. Then
= c - 3d,
= c - d,
= c + d,
= c + 3d. Then the sum of the four terms is 4d, and it equals 98, so c = 98/4 = 24.5 The sum of squares of the four terms is (c-3d)^2 + (c-d)^2 + (c+d)^2 + (c+3d)^2 = 3006 Making FOIL and combining like terms, you arrive to equation 4c^2 + 20d^2 = 3006, 4*24.5^2 + 20d^2 = 3006 20d^2 = 3006 - 4*24.5^2 = 605 d^2 = 605/20 = 30.25 d =
= +/- 5.5. Thus the four terms of the progression are 24.5-3*5.5 = 8, 24.5-5.5 = 19, 30, 41, if d= 5.5, and 24.5-3*(-5.5) = 41, 24.5-(-5.5) = 30, 19, 8, if d= -5.5. Thus the problem has two possible ANSWERS for the third term: it is EITHER 30 OR 19.
Solved.
Question 1187218: 7. Find the sum of
a) the positive multiples of 5 up to 500
b) the positive multiples of 7 up to 245
Answer by ikleyn(42188)
You can put this solution on YOUR website! Do part (b) in the same way.
.
7. Find the sum of
a) the positive multiples of 5 up to 500
b) the positive multiples of 7 up to 245
~~~~~~~~~~~~~~~` (a) S = 5 + 10 + 15 + . . . + 500 = 5*(1 + 2 + 3 + . . . + 100) =
= 5*50*101 = 25250. ANSWER Use the formula of the sum of the first n natural numbers 1 + 2 + 3 + . . . + n =
.
Part (a) is just solved.
Question 1187173: what is the nth term of the sequence 0,6,14,24,36,50,...
Answer by MathLover1(19110)
You can put this solution on YOUR website! find differences second differences are same, nth term formula is quadratic from eq.1 and eq.2 we have from eq.1 and eq.3 we have equal eq.1)) and eq.2)) go to
,
,
,
,
,
,.......
...
...
...
...
...
... ...
...
...
...
...... ......
......
......
..........solve for
....eq.1
............solve for
...........eq.2
............solve for
...........eq.3
.......solve for
..............eq.1))
.....solve for
.........divide by
............eq.2))
....solve for
..............eq.1), substitute
go to
....eq.1, substitute
and
th term formula is:
or
Question 1187153: ∞
∑n=0
(3+sinnθ)/10n
Answer by ikleyn(42188)
You can put this solution on YOUR website! Without having your question, I even can not hypothesize what you want from us, the tutors. It is very bad style to post something to this forum with no question. Such posts with no question submit to this web-address www.mad-house.homeworkHELP.com They accept everything with no objections, and for free.
.
Question 1186957: 2. Given that
(4 20)
2
n +
n
is the sum of the first n terms of an arithmetic sequence.
a) Write down the expression for the sum of the first
( 2) n − terms. [3 marks]
b) Find the first term and the common difference of the above sequence.
Answer by greenestamps(9971)
You can put this solution on YOUR website! Unreadable in that format. Type the information from your keyboard -- copy and paste often doesn't work. Re-post
Question 1186884: What is the next term in this sequence?
66 67 70 71 72 73 74 75 76 77
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(9971)
You can put this solution on YOUR website! The only way to get the right answer to any problem like this is to ask the person who created the problem what the right answer is. That is not mathematics. You can spend as much or as little time on any problem like this trying to find a logical rule or pattern that produces the given sequence of numbers -- but realize that any answer you come up with is only a guess. So, while it is nonsense to expect the reader to answer the question correctly, a problem like this can provide some useful mental exercise. Here is my GUESS: 100 rationale: the sequence is the increasing sequence of integers that can be written without using the digits 8 or 9. Note that the equivalent of that is to say the next number is 100 because the sequence is consecutive integers in base 8. I would say that, since that answer fits perfectly, there is a HIGH PROBABILITY that it is the expected answer.... But we can't know for sure
Answer by ikleyn(42188)
You can put this solution on YOUR website! This question is mathematically nonsensical. Any number can be next term. It is mathematically nonsensical BECAUSE there is NO logical connection between the given part and the question. The given part is irrelevant to the question and the question is irrelevant to the given part.
.
Question 1186636: a1=-10 and 2an-1
Answer by Alan3354(67840)
Question 1186602: 51, 53, 56, 60 what comes next? 51, 53, 56, 60, __, __
Found 4 solutions by greenestamps, ikleyn, Alan3354, MathLover1:
Answer by greenestamps(9971)
You can put this solution on YOUR website! Contrary to what two other tutors have said, it is not always true that this kind of problem is a waste of time. It is indeed true that any next number will make a valid sequence, as one tutor said. It is also true, as another tutor said, that we can find as many polynomial functions as we want that produce the given first four numbers and produce different subsequent numbers. So even with formal mathematical methods we can get an infinite number of different results for the next two numbers in the sequence. However, those facts do not make all problems like this a waste of time. Mathematics is full of wonderful (and wondrous) patterns. Good problems like this help teach a student to look for patterns. At this forum (and elsewhere) we see a great many problems like this that have no easily discernible pattern; THOSE problems are usually a waste of time. But this example has an obvious pattern which is PROBABLY the expected answer. True, we can't KNOW that it is the expected answer; but we can guess that it probably is. The pattern is that the differences between successive terms of the sequence increase by 1: Continue that pattern to find as many more terms of the sequence as you want:
51 + 2 = 53
53 + 3 = 56
56 + 4 = 60
60 + 5 = 65
65 + 6 = 71
71 + 7 = 78
etc...
Answer by ikleyn(42188)
You can put this solution on YOUR website! I can construct a polynomial of high degree, which will has given values in given points, An arbitrary person from the street can construct a polynomial even more hire degree As the question is posed in the post, IT MAKES the problem non-Mathematical. With such questions, you should go to fortune-tellers. Actually, such questions is the way for them to make money. More reasonable/educated people do not play such games . . . And do not ask such questions . . . //////////// "What is the pattern ?" would be correct, reasonable question in this context. Even better is to ask "what pattern do you see ?", because another person can see different pattern. "What is the next number", or "what comes next" is not correct or reasonable question in this context. ANY NUMBER CAN BE NEXT, if restrictions are not imposed. Also, to ask "predict next number, using a polynomial of lowest degree" is a correct question . . . Actually, at the level of common sense, all these things are SELF - EVIDENT . . . . . . They do not require special knowledge . . .
.
and totally different value in the next point.
and obtain different "next" number.
in this context, because it determines a procedure by an unique way.
Answer by Alan3354(67840)
Answer by MathLover1(19110)
You can put this solution on YOUR website!
sequence : .....
....
.....
First diff. : ...........
.....
Second diff. : ..........
We see that the second differences (blue ones) are all equal so we concludet that this is a quadratic sequence.
The quadratic sequence has the form
To find the value of we just divide second difference (
) by
.
Now we have:
Substitute and
into above equation:
---------------------------------------- Since and
, we have
....eq.1
.............e.2
---------------------------------------subtract eq.1 from eq.2
....... solve for
go to
....eq.1, substitute
....... solve for
and, your nth term formula is:
then next term will be 5th term, means
Question 1186524: A concert room has spaces for 10 seats in the first row, 13 in the second, 16 in the third, and so on.
a. If there are 20 rows in the theater, represent the total number of seats in the concert room in sigma notation.
b. What is the maximum number of seats that can be occupied in the said concert room?
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(9931)
You can put this solution on YOUR website!
A concert room has spaces for 10 seats in the first row, 13 in the second, 16 in the third, and so on.
a. If there are 20 rows in the theater, represent the total number of seats in the concert room in sigma notation.
b. What is the maximum number of seats that can be occupied in the said concert room?
Formula for the SUM of an AP:
, with
then becomes:
Maximum number of seats with 20 rows, or
Answer by ikleyn(42188)
You can put this solution on YOUR website! --------------- For introductory lessons on arithmetic progressions see Also, you have this free of charge online textbook in ALGEBRA-II in this site The referred lessons are the part of this online textbook under the topic Save the link to this textbook together with its description Free of charge online textbook in ALGEBRA-II into your archive and use when it is needed.
.
A concert room has spaces for 10 seats in the first row, 13 in the second, 16 in the third, and so on.
a. If there are 20 rows in the theater, represent the total number of seats in the concert room in sigma notation.
b. What is the maximum number of seats that can be occupied in the said concert room?
~~~~~~~~~~~~~~~~~~ (a) The sequence is the arithmetic progression with the first term a = 10; the common difference d = 3 and the number of terms n = 20. So, the formula for the n-th term of an arithmetic progression
=
+ (n-1)*d and it is the number of seats in the n-th row. The formula for the total number of seats is (sigma-notation) S =
. (b) To answer this question, apply the formula for the sum of n terms of an arithmetic progression
=
=
= 770.
Solved.
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
in this site.
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
Question 1186523: A student decides to follow a simple scheme to save money. She puts aside 5 peso the first day, 10 pesos the second day, 15 pesos the third day, 20 pesos the fourth day, and so on.
a. Following the pattern of how she saves money, how much will she put aside on the 30th day?
b. How much money will she have at the end of 30 days?
Answer by ikleyn(42188)
You can put this solution on YOUR website! --------------- For introductory lessons on arithmetic progressions see Also, you have this free of charge online textbook in ALGEBRA-II in this site The referred lessons are the part of this online textbook under the topic Save the link to this textbook together with its description Free of charge online textbook in ALGEBRA-II into your archive and use when it is needed.
.
A student decides to follow a simple scheme to save money. She puts aside 5 peso the first day,
10 pesos the second day, 15 pesos the third day, 20 pesos the fourth day, and so on.
a. Following the pattern of how she saves money, how much will she put aside on the 30th day?
b. How much money will she have at the end of 30 days?
~~~~~~~~~~~~~~~~~~ (a) Use the formula for the n-th term of an arithmetic progression.
= 5, d = 5, n= 30.
=
+ d*(n-1).
= 5 + 5*(30-1) = 5 + 5*30 - 5 = 5*30 = 150. ANSWER. 150 pesos. (b) Use the formula for the sum of the first n terms of an arithmetic progression. You know the first term
= 5, the last term
= 150 and the number of terms n = 30. So, you can use the simplest formula form
=
=
= use your calculator = 2325. ANSWER. 2325 pesos.
Solved and explained.
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
in this site.
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
Question 1186218: The sum of an infinite geometric series is 108, while the sum of the first 3 terms is 112. Determine the first term of this series.
Answer by greenestamps(9971)
You can put this solution on YOUR website! Let the first term be a and the common ratio be r. (1) The infinite sum is The sum of the first three terms is ANSWER: The first term is a = 144. CHECK: infinite sum: sum of first three terms:
Question 1185522: Find the missing term in harmonic sequence. Show the solution
___,1/2,2/5,1/3,___
Found 2 solutions by greenestamps, robertb:
Answer by greenestamps(9971)
You can put this solution on YOUR website! The response from tutor @robertb shows one way of solving a problem like this involving harmonic sequences. Here is a different way that I personally prefer. In a harmonic sequence, the terms can be written with a common NUMERATOR, and with DENOMINATORS that form an arithmetic sequence. So given the harmonic sequence ____, 1/2, 2/5, 1/3, ____ rewrite all the given terms with the same numerator: ____, 2/4, 2/5, 2/6, ____ Then the pattern is clear: 2/3, 2/4, 2/5, 2/6, 2/7 ANSWER: The missing numbers are 2/3 and 2/7
Answer by robertb(5830)
You can put this solution on YOUR website! 1/a, 2, 5/2, 3, 1/b are in AP. It is quite clear that 1/a = 3/2 and 1/b = 7/2. (The common difference is 1/2.) ===> a = 2/3 and b = 2/7.
If the numbers a, 1/2, 2/5, 1/3, b are in harmonic progression, then their reciprocals are in arithmetic progression, i.e.,
Question 1186084: Problem solving. Solve the word problem below and show your solution.
A ball is dropped from the top of a building that is 20 meters high. If the ball rebounds to a height that is half tall of its previous height every time it hits the ground. What is the total distance travelled by the ball before coming to rest?
Answer by Edwin McCravy(18936)
You can put this solution on YOUR website!
It falls down 20 meters, then up 10 meters. So its first "down+up" is 30 meters. Then it falls down 10 meters then up 5 meters. So its second "down+up" is 15 meters. So we have an infinite geometric series with a1 = first term = 30 and r = common ratio = 1/2. The formula for the sum of any infinite geometric series is:
Substituting:
Edwin
Question 1186080: Find the missing term in geometric sequence.
-1/3,___,-4/45,___,8/135,___.
Answer by ikleyn(42188)
You can put this solution on YOUR website! This sequence IS NOT a geometric sequense.. The question is not SELF-CONSISTENT; it is SELF-CONTRADICTORY.
.
Find the missing term in geometric sequence.
-1/3,___,-4/45,___,8/135,___.
~~~~~~~~~~~~~~~~~~~~~~~
Question 1186075: Find the missing terms of the geometric sequence.
0.3,___,2.7,___,___.
Answer by josgarithmetic(36644)
(Show Source): Question 1186074: Find the arithmetic mean of the following. Show the solution
1. 8 and 26
2. 24 and 54
Answer by ikleyn(42188)
You can put this solution on YOUR website!
.
1. Add 8 and 26; then divide the sum by 2. 2. Add 24 and 54; then divide the sum by 2.
That's all.
Question 1186057: Find the common ratio of the geometric sequence 3, __, __, __, -5,625
Answer by ikleyn(42188)
You can put this solution on YOUR website! This sequence IS NOT a geometric progression. The question is not SELF-CONSISTENT; it is SELF-CONTRADICTORY.
.
Question 1186017: Find the missing terms in each geometric sequence.
1. ___,___,-16,4,-1
2. 625,___,25,___,1
3. 0.3,___,2.7,___,___.
4. -1/3,___,-4/45,___,8/135,___.
It's okay if there's no solution please help.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(42188)
You can put this solution on YOUR website!
.
In part (2), the ratio of the third term to the first term gives you r^2 =
, which gives TWO possible values for the common ratio r =
and r =
. They have EQUAL RIGHTS and produce TWO possible geometric sequences. One sequence is 625, 125, 25, 5, 1. The other sequence is 625, -125, 25, -5, 1. So, there are two answers and two possible geometric sequences, instead of one, as proclaimed by @Edwin. Similar notice goes to part (3). Regarding part (4), it is not geometric sequence, at all. So, you ONLY CAN reject it . . .
Answer by Edwin McCravy(18936)
You can put this solution on YOUR website!
1. ___,___,-16,4,-1 4 over -16 is -4/16 which reduces the -1/4 -1 over 4 is also -1/4 So the blank left of 16 is something so that if you multiply it by -1/4 you get -16. If it is x then
Can you solve that? If you can, then the first blank is something so that if you multiply it by -1/4 you get what you got for the second blank. 2. 625,___,25,___,1 If the common ratio is r, the
goes in the second blank 625, 625r,25,___,1 So (625r)(r)=25 625r2=25 r2=25/625 r=5/25 r=1/5 So what does 625r equal? Multiply 25 by r to get what goes in the other blank 3. 0.3,___,2.7,___,___. That's the same way as 2, except it uses decimals instead of fractions. 4. -1/3,___,-4/45,___,8/135,___. You can do that one. Edwin
Question 1186018:
Answer by ikleyn(42188)
Question 1185948: 48 16 21 7
Found 3 solutions by ikleyn, greenestamps, Edwin McCravy:
Answer by ikleyn(42188)
You can put this solution on YOUR website! I am very surprised that two respectful maestro tutors discuss this gibberish instead of deleting it . . .
.
Answer by greenestamps(9971)
You can put this solution on YOUR website! The post comes without a question, so there can be no answer.... Assuming the problem is to find the next term (or next few terms) of the sequence, another tutor has used the given numbers to determine one POSSIBLE pattern for producing the sequence: "divide by 3; add 5; repeat". However, that is not THE answer to the problem; it is only one of an infinite number of possible answers. ANY subsequent numbers will form a valid sequence.... In ANY problem like this, if only numbers are given, without any information about what kind of sequence it is, then there is no way to know what "the" answer is. It is only a guessing game; it is not mathematics.
Answer by Edwin McCravy(18936)
You can put this solution on YOUR website!
Start with 48, then divide by 3, get 16 add 5, get 21 divide by 3, get 7 add 5, get 12 divide by 3, get 4 add 5, get 9 divide by 3, get 3 add 5, get 8 then it gets into fractions. Edwin
Question 1185530: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x) → 0.]
f(x) = ln(1 + 2x)
Answer by robertb(5830)
Question 1185813: Insert 2 arithmetic means between 10 and 37.
Answer by ikleyn(42188)
You can put this solution on YOUR website!
.
Imagine yourself working on the number line. When you insert two arithmetic means between the points 10 and 37, you get 3 (three) intervals of equal length on the segment [10,37], whose length is 37-10 = 27 units. These three segments have the same length, so the length of each small segment is 27/3 = 9 units. This length of small segments is nothing else as the common difference of the arithmetic progression. HENCE, you have an arithmetic progression 10, 19, 28, 37, and the inserted arithmetic means are the points (the values) 19 and 28.
Solved.
Question 1185523: Insert the indicated number of harmonic means given the first and last terms. Show the solution.
1/2 and 1/6 [3] or insert 3
2/3 and 2/9 [2] or insert 2
5/2 and 5/27 [4] or insert 4
Answer by robertb(5830)
You can put this solution on YOUR website!
I will do the first progression only-- insert 3 harmonic means between 1/2 and 1/6.
If five numbers are in harmonic progression then their reciprocals are in arithmetic progression.
Let those numbers in AP be 2, a, b, c, 6.
Then it's quite clear that the numbers in between are 2, ,
,
, 6.
Therefore the three harmonic means between 1/2 and 1/6 are 1/3, 1/4, and 1/5.
Question 1185725: Please help me solve this
1-((2-1)/4)-((2^2-1)/4^2)-((2^3-1)/4^3)-((2^4-1)/4^4)- infinite
Found 2 solutions by robertb, greenestamps:
Answer by robertb(5830)
Answer by greenestamps(9971)
You can put this solution on YOUR website! 1 - ((2-1)/4) - ((2^2-1)/4^2) - ((2^3-1)/4^3) - ((2^4-1)/4^4) - ... 1 - 1/4 - (4-1)/16 - (8-1)/64 - (16-1)/256 - ... 3/4 - (4/16-1/16) - (8/64-1/64) - (16/256-1/256) - ... 3/4 - (4/16+8/64+16/256...) + (1/16+1/64+1/256...) The two expressions in parentheses are infinite geometric sequences with common ratio less than 1. 4/16+8/64+16/256+... = 1/4+1/8+1/16+... = (1/4)/(1-1/2) = (1/4)/(1/2) = (1/4)(2/1) = 1/2 1/16+1/64+1/256+... = (1/16)/(1-1/4) = (1/16)/(3/4) = (1/16)(4/3) = 1/12 The sum of the sequence is then 3/4 - 1/2 + 1/12 = 9/12 - 6/12 + 1/12 = 4/12 = 1/3 ANSWER: 1/3
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Mathematics Enhanced Scope And Sequence Algebra Ii Answers
Source: https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq
Posted by: mitchelltheinder1941.blogspot.com
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