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The first and the 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?
The first and the 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?
Updated On: Jan 13, 2026
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Solution and Explanation
Given \(a = 17\), \(l = 350\), and \(d = 9\), let there be n terms in the A.P.
Using the formula \(l = a + (n − 1) d\), we substitute the given values: \(350 = 17 + (n − 1)9\).
Subtracting 17 from both sides gives \(333 = (n − 1)9\).
Dividing by 9 yields \(n − 1 = 37\).
Therefore, \(n = 38\).
The sum of the series is calculated using \(S_n = \frac n2[a + l]\).
\(S_n = \frac {38}{2}[17 + 350] = 19 \times 367 = 6973\).
This A.P. consists of 38 terms, and their sum is 6973.
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