Question

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Answer 1

Since 105, 110, 115,…………995 are the numbers lying between 100 and 1000, are multiples of 5. 

∴ Required sum =105 + 110 + 115 + ……………….+ 995. 

This series in A.P.with a_n =105. 

d = 110 - 105 = 5 and a_n = 995. 

We have, 

a_n = a, + (n -1 )d 

⇒ 995 = 105 + (n -1)(5) 

⇒ 995 = 105 + 5/1 - 5 

⇒ 895 = 5n