The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Let there be n terms in the A.P.

Given,

First term (a) = 17

Last term (l) = a_n = 350

Common difference (d) = 9

By formula,

a_n = a + (n - 1)d

Substituting values we get :

⇒ 350 = 17 + 9(n - 1)

⇒ 350 = 17 + 9n - 9

⇒ 350 = 9n + 8

⇒ 9n = 350 - 8

⇒ 9n = 342

⇒ n = $\dfrac{342}{9}$ = 38.

By formula,

Sum of A.P. (S) = $\dfrac{n}{2}(a + l)$

Substituting values we get :

$\text{Sum of first 38 terms} = \dfrac{38}{2}(17 + 350) \\[1em] = 19 \times 367 \\[1em] = 6973.$

Hence, sum of A.P. = 6973 and number of terms = 38.