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}=2^9Question:

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.