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 = $\dfrac{n}{2}[2a + (n - 1)d]$

⇒ S₁₆ = $\dfrac{16}{2}[2 \times 6 + 6(16 - 1)]$
⇒ S₁₆ = 8[12 + 90]
⇒ S₁₆ = 8 × 102
⇒ S₁₆ = 816.

Hence, the sum of all natural numbers less than 100 which are divisible by 6 is 816.