Problem: In a certain sequence of numbers, the first number in the sequence is I, and, for all n≥2, the product of the first n numbers in the sequence is n2. The sum of the third and the fifth numbers in the sequence is
Answer Choices:
A. 925
B. 1531
C. 1661
D. 225576
E. 34
Solution:
If an denotes the nth number in the sequence, then
an=a1a2⋯an−1n2a1a2⋯an=(n−1)2n2
for n≥2. Thus, the first five numbers in the sequence are 1,4,49,916,1625, and the desired sum is 49+1625=1661.