Find the sum of all natural numbers that are less than 100 and divisible by 4.

Natural no less than 100 and are divisible by 4 are 4, 8, 12, 16, …, 96

Clearly this is an AP, with

First term, a = 4

Common difference, d = 4

Last term or nth term, a_n = 96

We know that, nth term of an AP is,

a_n = a + (n - 1)d

where a is first term and d is common difference of AP

Putting values, we get

96 = 4 + (n - 1)4

⇒ 92 = 4n - 4

⇒ 96 = 4n

⇒ n = 24

Also, sum of an AP if first and nth term are given,

Where, a is first and a_n is nth term