Question

Find the sum of all natural numbers lying between 100 and 200 which leave a remainder of 2 when divided by 5 in each case.

Answer 1

The natural number which leaves remainder 2 greater than 100 is 102, and less than 200 is 197.

The series is 102, 107, 112, 117, 122, .... , 197.

Number of terms

$=\frac{200}{5}-\frac{100}{5}=40-20=20$

$S_n=\frac{n}{2}[a+l]=\frac{20}{2}[102+197]=2990$