Find the sum of first 100 even natural numbers which are divisible by 5.

Question

Philoid · Accepted Answer

First 100 even natural numbers which are divisible by 5 are 10, 20, 30, …, 1000

Here, first term = a = 10

Common difference = d = 10

Number of terms = 100

Now, Sum of n terms of this arithmetic series is given by:

S_n = [2a + (n - 1)d]

Therefore sum of 100 terms of this arithmetic series is given by:

∴ S₁₀₀ = [2(10) + (100 - 1)(10)]

= 50 × [20 + 990]

= 50 × 1010

= 50500