What is the first term of an arithmetic progression of positive integers?
I. Sum of the squares of the first and second term is $116$.
II. The fifth term is divisible by $7$.
Since 116 is less than 112, it can be figured out that both the first two terms of the AP should be less than 10.
Since, there is only one pair of positive integers whose squares add up to 116 and they are 10 and 4.
Hence, these two should be the first two terms of the AP. The first term hence is 4, and can be obtained only from statement I.
Option D is the Correct Answer.