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​=a1​a2​⋯an−1​n2​a1​a2​⋯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​.