In the sequence \(S_1, S_2, S_3, \ldots,S_n \),

[M7MBA]

In the sequence \(S_1, S_2, S_3, \ldots,S_n \),

\(S_m = S_{m−1} + S_{m−2}\) for all \(m > 2.\)

If \(S_1 = 0\) and \(S_{n−1}= 8S_2,\) how many terms does the sequence have?

A) 8
B) 9
C) 10
D) 11
E) 12

[spoiler]OA=A[/spoiler]

Source: e-GMAT

[Jay@ManhattanReview]

In the sequence \(S_1, S_2, S_3, \ldots,S_n \),

\(S_m = S_{m−1} + S_{m−2}\) for all \(m > 2.\)

If \(S_1 = 0\) and \(S_{n−1}= 8S_2,\) how many terms does the sequence have?

A) 8
B) 9
C) 10
D) 11
E) 12

[spoiler]OA=A[/spoiler]

Source: e-GMAT

From \(S_m = S_{m−1} + S_{m−2}\), we have \(S_3 = S_2 + S_1=S_2\)

Again, \(S_4 = S_3 + S_2=S_2+S_2 = 2S_2\)

Again, \(S_5 = S_4 + S_3=2S_2+S_2=3S_2\)

With this way, \(S_7 = 8S_2\)

=> \(7 = n-1=> n = 8\)

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes Albuquerque | GMAT Tutoring | LSAT Prep Courses El Paso | Oakland Prep Classes SAT | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.