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

Given, a = 17, l = 350 and d = 9.

Let nth be the last term so,
l = a_n = 350

By formula, a_n = a + (n - 1)d
⇒ 350 = 17 + (n - 1)9
⇒ 350 = 17 + 9n - 9
⇒ 350 = 9n + 8
⇒ 9n = 350 - 8
⇒ 9n = 342
⇒ n = 38.

By formula, S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

⇒ S₃₈ = $\dfrac{38}{2}[2 \times 17 + (38 - 1)9]$
⇒ S₃₈ = 19[34 + 37(9)]
⇒ 19[34 + 333]
⇒ 19(367)
⇒ 6973.

Hence, number of terms = 38 and the sum of the terms = 6973.