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

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 last term can be written as;

\(\Rightarrow \) l = a+(n - 1)d
\(\Rightarrow \) 350 = 17+(n - 1)9
\(\Rightarrow \) 333 = (n -1)9
\(\Rightarrow\) (n- 1) = 37
\(\Rightarrow \) n = 38
\(\Rightarrow S_n = {{n} \over {2}} (a+l)\)
\(\Rightarrow S_{38} = {{13} \over {2}} (17+350)\)
= 19×367
= 6973

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