Q. 125.0( 1 Vote )

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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