Question

Find the sum of the integers between 100 and 200 that are not divisible by 9

Answer 1

The sum of the integers between 100 and 200 which is not divisible by 9 = (sum of total numbers between 100 and 200) – (sum of total numbers between 100 and 200 which is divisible by 9)  ........(i)

Total numbers between 100 and 200 is 101, 102, 103,

199

Here, a = 101, d = 102 – 101 = 1 and

a_n = l = 199

⇒ 199 = 101 + (n – 1)1  ......[∵ a_n = l = a + (n – 1)d]

⇒ (n – 1) = 98

⇒ n = 99

Sum of terms between 100 and 200,

`S_n = n/2[2a + (n - 1)d]`

⇒ `S_99 = 99/2[2(101) + (99 - 1)1]`

= `99/2[202 + 98]`

= `99/2 xx 300`

= `99 xx 150`

= 14850

From equation (i) sum of the integers between 100 and 200 which is not divisible by 9

= 14850 – 1683  ......[From part (i)]

= 13167

Hence, the required sum is 13167