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# The First and the Last Terms of an A.P. Are 8 and 350 Respectively. If Its Common Difference is 9, How Many Terms Are There and What is Their Sum? - Mathematics

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The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

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#### Solution

First term, a = 8

Common difference, d = 9

Let the nth term be the last term.

∴ l = an = 350

⇒ a + (n − 1) d = 350

⇒ 8 + (n − 1) × 9 = 350

⇒ (n − 1) × 9 = 342

rArr n-1=342/9=38

rArrn=38+1=39

Thus, there are 39 terms in the given A.P.

Sum of 39 trems , S_39=39/2(a+a_39)

=39/2xx(8+350)

=39/2xx358

=6981

Concept: Sum of First n Terms of an AP
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