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?

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#### Solution

Given that,

*a* = 17

*l* = 350

*d* = 9

Let there be *n* terms in the A.P.

*l = a + *(*n* − 1) *d*

350 = 17 + (*n* − 1)9

333 = (*n* − 1)9

(*n* − 1) = 37

*n* = 38

`S_n = n/2(a+l)`

`=>S_n=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.

Concept: Sum of First n Terms of an AP

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