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# Find the sum of all numbers between 100 and 200 which are not divisible by 5.

Answer :

We first find the sum of all numbers divisible by 5

Series of all natural numbers divisible by 5 between 100and 200 is:

105, 110,………………………………195

In the A.P.

First term = 105

Last term = 195

Common difference = 5

Nth term = a + (n–1) d

⇒ 195 = 105 + (n–1)5

⇒ 90 = (n–1)5

⇒ 18 = (n–1)

⇒ n = 19

Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms =

⇒ Sum of terms = 2850

Sum of 101,102….199 = Sum of 199 natural numbers – Sum of 100 natural numbers

⇒ Sum(101, 102,…. 199) =

⇒ Sum(101, 102,…. 199) = 19900–5050 = 14850

Sum of all numbers between 100 and 200 not divisible by 5 = 14850–2850 = 12000

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