Find the sum of all natural numbers less than 100 which are divisible by 6.

The sum of all natural numbers less than 100 which are divisible by 6 is given as 6 + 12 + 18 + .... + 96. The above series is an A.P. with a = 6, d = 6 and l = 96. Let 96 be nth term of the series then, ⇒ 96 = 6 + 6(n - 1) ⇒ 96 - 6 = 6n - 6 ⇒ 90 = 6n - 6 ⇒ 6n = 90 + 6 ⇒ 6n = 96 ⇒ n = 16. By formula S n = ⇒ S 16 = ⇒ S 16 = 8[12 + 90] ⇒ S 16 = 8 × 102 ⇒ S 16 = 816. Hence, the sum of all natural numbers less than 100 which are divisible by 6 is 816.

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Mathematics

Find the sum of all natural numbers less than 100 which are divisible by 6.

AP GP

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