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.