Find the sum of the integers between 100 and 200 that are

divisible by 9.

Given: integers between 100 and 200.

To find: Sum of integers between 100 and 200 divisible by 9.

Formula Used:

Sum of “n” terms of an AP:

Where S_n is the sum of first n terms

nth term of an AP is:

a_{n =} a + (n - 1) d

Where a_n is the last term.

n = no of terms

a = first term

d = common difference

Explanation:

The number (integers) between 100 and 200 which is divisible by 9 are 108, 117, 126, …198

Let n be the number of terms between 100 and 200 which is divisible by 9.

Then,

a_n = a + (n - 1) d

198 = 108 + (n - 1 )9

90 = (n - 1 )9

n - 1 = 10

n = 11

now, Sum of this AP

[ as last term is given]

= 11(153)

= 1683