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Question
The first and last terms 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
9n = 350 + 9 – 17
9n = 359 – 17
9n = 342
⇒ n = `342/9`
⇒ n = 38
Sn = `n/2 (a + l)`
Sn = `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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