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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]

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New post Updated on: 21 Mar 2012, 05:51
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Question Stats:

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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

Originally posted by BN1989 on 21 Mar 2012, 05:18.
Last edited by Bunuel on 21 Mar 2012, 05:51, 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]

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New post 21 Mar 2012, 06:36
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]

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New post 10 Apr 2014, 04:06
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
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Re: Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2  [#permalink]

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New post 18 Sep 2014, 12:14
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


Sol:
I wanted to check what would be sum of 4 terms(n=4) based on that I can assume final answer:

2+2+2^2+2^3

2(1+1+2+2^2)= 2(2+2+2^2)= 2*2(1+1+2)= 2*2*2*2=2^4 =>2^n

so sum or n terms where n=10 willbe 2^10
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Re: Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2   [#permalink] 18 Sep 2014, 12:14
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Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2

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