Find the sum of the first 40 positive integers divisible by 6.

List of positive integers divisible by 6 are :

6, 12, 18, ……..

The above list is an A.P. with first term (a) = 6 and common difference (d) = 12 - 6 = 6.

By formula,

Sum of first n terms = S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

Substituting values we get :

$S_{40} = \dfrac{40}{2}[2 \times 6 + (40 - 1) \times 6] \\[1em] = 20 \times [12 + 39 \times 6] \\[1em] = 20 \times [12 + 234] \\[1em] = 20 \times 246 \\[1em] = 4920.$

Hence, sum of first 40 positive integers divisible by 6 = 4920.