Find the sum of the following series.

7 + 14 + 21…. + 490

Given the series S = 7 + 14 + 21…. + 490,

We see that there is a common term 7 in all the numbers in the series. Taking 7 common, we have

S = 7(1 + 2 + 3 + .. + 70)

Let 1 + 2 + 3 + .. + 70 be S₁, with n = 70

So S becomes S = 7S₁

To find S₁-

Formula for sum of first n numbers is

S₁ =

35 × 71

= 2485

S = 7S₁

S = 7 × 2485 = 17395

The sum S = 7 + 14 + 21…. + 490 = 17395