If \(S_n\) is the sum of first \(n\) terms of a certain sequence and \(S_n = n (n^2 + 1)\) for all positive integers. What is the \(4th\) term of the sequence?
A. 10
B. 20
C. 38
D. 66
E. 68
Answer: C
Source: e-GMAT
If \(S_n\) is the sum of first \(n\) terms of a certain sequence and \(S_n = n (n^2 + 1)\) for all positive integers.
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
GIVEN: Sn is the sum of first n terms of a certain sequence
So, for example,
S4 = term1 + term2 + term3 + term4
S3 = term1 + term2 + term3
This means that S4 - S3 = (term1 + term2 + term3 + term4) - (term1 + term2 + term3 )
= term4
Perfect, we now know that term4 = S4 - S3
According to the formula for Sn, we know that:
S4 = 4(4² + 1) = 4(16 + 1) = 68
S3 = 3(3² + 1) = 3(9 + 1) = 30
We can now write: term4 = 68 - 30 = 38
Answer: C
Cheers,
Brent