Carcass wrote:
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
GIVEN: Sn is the sum of first n terms of a certain sequenceSo, for example,
S4 = term1 + term2 + term3 + term4S3 = 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) = 68S3 = 3(3² + 1) = 3(9 + 1) = 30 We can now write:
term4 =
68 -
30 = 38
Answer: C
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep