Question

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?

Answer 1

Given that, \(a = 17\), \(l = 350\) and \(d = 9\)
Let there be n terms in the A.P.
\(l = a + (n − 1) d\)
\(350 = 17 + (n − 1)9\)
\(333 = (n − 1)9\)
\(n − 1 = 37\)
\(n = 38\)
\(S_n = \frac n2[a + l]\)

\(S_n = \frac {38}{2}[17 + 350] = 19 \times  367 = 6973\)

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