given an AP is required of all integers between 100 and 800, which on division by 16 leaves remainder 7

To find: the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7

So, the sequence is 103, 119, 135….791

It is an AP whose first term is 103 and d is 16

Hence the sum is given by the formula

Now for the finding number of terms, the formula is

n = 44

substituting n in the sum formula, we get

s = 19668