Question

Find the sum of the integers between 100 and 200 that are divisible by 5.

Answer 1

Method of Solution :

Integers between 100 and 200 which are divisible by 5 : 105,110 ,115 ........195

Here, First term of AP = 105

Common difference = 110 - 105 => 5

Now, According to the Question's Statement!

Statement : Sum of the integers between 100 and 200 that are divisible by 5.

Required A . P = 105 + 110 + 115 + ......... + 195

Tn = a + (n-1)d

195 ✏ 105 + (n-1)5

✒ 195 = 105 + 5n - 5

✒ 195 = 100 + 5n

✒ n = 95 /5

✒ n = 19

Now, Applying Summation Formula!

Sn = n/2(a+l)

Sn = 19/2(105 + 195)

Sn = 19/2 × 300

Sn = 19 × 150

Sn = 2850

Hence, Required Sum of the integers between 100 and 200 that are divisible by 5 is $\bf{\huge{28,50}}$