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

We have; a = 17, a_n = 350 and d = 9

We know;

a_n = a + (n – 1)d

350 = 17 + (n – 1)9

(n – 1)9 = 350 – 17

n – 1 = 333/9 = 37

n = 38

Now, sum can be calculated as follows:

= 19*367

= 6973