Find the sum of all 2-digit natural numbers divisible by 5.

The 2-digit natural numbers divisible by 5 form an A.P., with common difference = 5.

10, 15, 20,…..,95

Let total number of terms in an A.P. be n.

We know that,

∴ a_n = a + (n - 1)d

⇒ 95 = 10 + (n - 1)5

⇒ 95 - 10 = (n - 1)5

⇒ 85 = (n - 1)5

⇒ $\dfrac{85}{5}$ = (n - 1)

⇒ 17 = (n - 1)

⇒ n = 17 + 1

⇒ n = 18.

We know that,

Sum of n terms of an A.P. is given by,

∴ S_n = $\dfrac{n}{2}$ (a + l)

⇒ S₁₈ = $\dfrac{18}{2} \times (10 + 95)$

= 9(105)

= 945.

Hence, S₁₈ = 945.