Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60 ..... is 300 ? Hence find the sum of all terms of the Arithmetic Progression (A.P.).

Given,

A.P. : 15, 30, 45, 60 .....

First term (a) = 15

Common difference (d) = 30 - 15 = 15

Let n^th term be 300.

⇒ a_n = 300

⇒ a + (n - 1)d = 300

⇒ 15 + 15(n - 1) = 300

⇒ 15 + 15n - 15 = 300

⇒ 15n = 300

⇒ n = $\frac{300}{15}$ = 20.

Sum of the terms of the given A.P. :

⇒ S_n = $\frac{n}{2}(a + a_n)$

⇒ S₂₀ = $\frac{20}{2}(15 + 300)$

= 10 × 315

= 3150.

Hence, sum of all terms of the given A.P. = 3150.