In the sequence $S_1, S_2, S_3, ..., S_n$ , $S_m = S_{m-1}+S_{m-2}$ for all $m > 2$ . If $S_1=0$ and $S_{n-1}=8S_2$ , how many terms does the sequence have?

Correct answer marked below

Correct

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Comments

LilianAug 21

Took me a second to realize this is Fibonacci-like but with S1=0. Setting S2 as a variable made it click.

EugenioAug 26

Same here, once I wrote out the first few terms in terms of S2 it was way easier.

ShoilayeeAug 31

Yeah, the 8S2 was the hint for me to scale everything.

GiannaJul 21

Is n-1 always even here? I got confused whether the subscript parity matters when solving for n.

LokeshJul 25

Look at the coefficient of S2 in each term, it follows its own pattern. That should clear it up.

TrevorJun 29

This is a nice 700-level twist on a standard recurrence. Not hard once you see the pattern, but the algebra can eat time if you don't organize it.

TanyaJul 3

Agreed, I burned almost 3 minutes because I didn't set S2 = x right away.

RaghavAug 10

Why isn't the answer 10? I think I'm off by one on n vs n-1.

AdityaAug 11

Careful, S_{n-1} is not the last term. Count how many terms come before it.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

In the sequence S1,S2,S3,...,SnS_1, S_2, S_3, ..., S_nS1​,S2​,S3​,...,Sn​, Sm=Sm−1+Sm−2S_m = S_{m-1}+S_{m-2}Sm​=Sm−1​+Sm−2​ for all m>2m > 2m>2. If S1=0S_1=0S1​=0 and Sn−1=8S2S_{n-1}=8S_2Sn−1​=8S2​, how many terms does the sequence have?