Find the sum of all natural numbers between 100 and 200 which are divisible by 4.

The sum of natural numbers between 100 and 200 that are divisible by 4 is 104 + 108 + 112 + ..... + 196. The above series is an A.P. with a = 104, d = 108 - 104 = 4 and l = 196. Let 196 be nth term then, ⇒ 196 = 104 + 4(n - 1) ⇒ 196 - 104 = 4n - 4 ⇒ 92 = 4n - 4 ⇒ 4n = 92 + 4 ⇒ 4n = 96 ⇒ n = 24. By formula S n = ⇒ S 24 = ⇒ S 24 = 12[208 + 92] ⇒ S 24 = 12 × 300 ⇒ S 24 = 3600. Hence, the sum of all two digits natural numbers between 100 and 200 which are divisible by 4 is 3600.

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Mathematics

Find the sum of all natural numbers between 100 and 200 which are divisible by 4.

AP GP

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