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 *n*^{th} term be the last term.

∴ *l* = *a*_{n} = 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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