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?

Solution:

Given that,

First term, a = 17

Last term, l = 350

Common difference, d = 9

Let there be n terms in the A.P., thus the formula for the last term can be written as;

l = a + ( n − 1) d

350 = 17 + ( n − 1)9

333 = ( n − 1)9

( n − 1) = 37

n = 38

S_n = n /2 ( a + l )

S₃₈ = 38/2 (17 + 350)

= 19 × 367

= 6973

Thus, this A.P. contains 38 terms and the sum of the terms of this AP is 6973.