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Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2

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Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2 [#permalink] New post 21 Mar 2012, 04:18
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Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2^(n-1). What is the sum of the terms in sequence S when n=10?

A. 2^9
B. 2^10
C. 2^16
D. 2^35
E. 2^36

I think this is a weird question. First of all, shouldn't S1 be equal to 1 and not 2?

And even if S1 is 2, i still get 2^11 as the sum of all the terms.

source: gmathacks
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2012, 04:51, edited 1 time in total.
Edited the question
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Re: Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2 [#permalink] New post 21 Mar 2012, 05:36
Expert's post
BN1989 wrote:
Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2^(n-1). What is the sum of the terms in sequence S when n=10?

A. 2^9
B. 2^10
C. 2^16
D. 2^35
E. 2^36

I think this is a weird question. First of all, shouldn't S1 be equal to 1 and not 2?

And even if S1 is 2, i still get 2^11 as the sum of all the terms.

source: gmathacks


This question has quite a poor wording.

First of all: formula for n_{th} term, S_n=2^{n-1}, should state that it's for n>1 (so for the second term and onward). Next I guess the question asks about the sum of the first 10 terms.

Given:
S_1=2;
S_2=2;
S_3=2^2;
S_4=2^3;
...
S_{10}=2^9

Question: 2+2+2^2+2^3+...+2^9=?

Notice that: 2+2=2^2 (the sum of the first 2 terms), 2^2+2^2=2^3 (the sum of the first 3 terms), 2^3+2^3=2^4 (the sum of the first 4 terms), so with similar logic the sum of the first 10 terms will be 2^{10}.

Answer: B.

Another approach:

We have the sum of 10 terms. Now, if all terms were equal to the largest term 2^9 we would have: sum=10*2^9\approx{2^4*2^9}=2^{13}, so the actual sum is less than 2^{13} but more than 2^9 (option A). So the answer is clearly B.

Answer: B.
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Re: Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2 [#permalink] New post 10 Apr 2014, 03:06
Bunuel wrote:
BN1989 wrote:
Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2^(n-1). What is the sum of the terms in sequence S when n=10?

A. 2^9
B. 2^10
C. 2^16
D. 2^35
E. 2^36

I think this is a weird question. First of all, shouldn't S1 be equal to 1 and not 2?

And even if S1 is 2, i still get 2^11 as the sum of all the terms.

source: gmathacks


This question has quite a poor wording.

First of all: formula for n_{th} term, S_n=2^{n-1}, should state that it's for n>1 (so for the second term and onward). Next I guess the question asks about the sum of the first 10 terms.

Given:
S_1=2;
S_2=2;
S_3=2^2;
S_4=2^3;
...
S_{10}=2^9

Question: 2+2+2^2+2^3+...+2^9=?

Notice that: 2+2=2^2 (the sum of the first 2 terms), 2^2+2^2=2^3 (the sum of the first 3 terms), 2^3+2^3=2^4 (the sum of the first 4 terms), so with similar logic the sum of the first 10 terms will be 2^{10}.

Answer: B.

Another approach:

We have the sum of 10 terms. Now, if all terms were equal to the largest term 2^9 we would have: sum=10*2^9\approx{2^4*2^9}=2^{13}, so the actual sum is less than 2^{13} but more than 2^9 (option A). So the answer is clearly B.

Answer: B.


From 2nd term this is becoming geometric sequence.

2+ 2(2^9-1)/2-1

2+( 2*2^9 -2)

2^10
Re: Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2   [#permalink] 10 Apr 2014, 03:06
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Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2

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