Question

Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ______.

Answer 1

The correct answer is 53
$d_1=\frac{199−100}{2}∉I$
$d_2=\frac{199−100}{3}=33$
$d_3=\frac{199−100}{4}∉I$
$d_n=\frac{199−100}{i+1}∈I$
di= 33 + 11, 9
Sum of CD’s = 33 + 11 + 9
= 53