The first and the last term of an AP are 17 and 350 respectively
Question.

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:

Given that,

$a=17$

$\ell=350$

d = 9

Let there be n terms in the A.P.

$\ell=a+(n-1) d$

350 = 17 + (n – 1)9

333 = (n – 1)9

(n – 1) = 37

n = 38

$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+\ell)$

$\Rightarrow S_{n}=\frac{38}{2}(17+350)=19(367)=6973$

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