Q12 of 110 Page 53

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

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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