BTGModeratorVI wrote: ↑Wed Apr 22, 2020 11:11 am
If Sn is the sum of first n terms of a certain sequence and Sn = 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
Solution:
If we let a1, a2, a3, … be the terms of the sequence, we should recognize that S1 = a1, S2 = a1 + a2, S3 = a1 + a2 + a3, and so on. Therefore, using the formula given for Sn, we have:
S1 = 1(1^2 + 1) = 1(2) = 2 = a1 → a1 = 2
S2 = 2(2^2 + 1) = 2(5) = 10 = a1 + a2 → 10 = 2 + a2 → a2 = 8
S3 = 3(3^2 + 1) = 3(10) = 30 = a1 + a2 + a3 → 30 = 2 + 8 + a3 → a3 = 20
S4 = 4(4^2 + 1) = 4(17) = 68 = a1 + a2 + a3 + a4 → 68 = 2 + 8 + 20 + a4 → a4 = 38
Alternate Solution:
If we let a_n be the nth term of the sequence, we should recognize that a_1 = S_1 and for n > 1, a_n = S_n - S_(n - 1).
Since we are looking for a_4, using the formula given for S_n, we have:
a_4 = S_4 - S_3
a_4 = 4(4^2 + 1) - 3(3^2 + 1)
a_4 = 4(17) - 3(10) = 68 - 30 = 38
Answer: C
