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?
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?

Solution:

Provided that,

The first term, a = 17

The last term, l = 350

The common difference, d = 9

If the A.P. has n terms, the formula for the last term can be expressed as;

l = a+(n −1)d

350 = 17+(n −1)9

333 = (n−1)9

(n−1) = 37

n = 38

Sn = n/2 (a+l)

S38 = 13/2 (17+350)

= 19×367

= 6973 As a result, this A.P. has 38 terms, and the total number of terms in this A.P. is 6973.