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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