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?

Here, a = 17, a_n = 350 and d = 9.
a_n = a + (n – 1)d
⇒ 350 = 17 + (n -1)9
⇒ 350 = 8 + 9n
⇒ n = 342/9 = 38
The sum of n terms of an AP is given by
S_n = n/2[a + a_n]
⇒ S₃₈ = 38/2[17 + 350]
⇒ S₃₈ = 19 × 367
= 6973
Hence, there are 38 terms and their sum is 6973.