The n^th term if an AP is 5n + 2, then the sum of first n terms of the AP will be __________(a) \(\frac {n^2 – 8}{2}\)(b) \(\frac {n^2 + 8}{2}\)(c) \(\frac {n^2 – 9}{2}\)(d) \(\frac {n^2 + 9}{2}\)I got this question during an internship interview.The question is from Sum of N Terms of Arithmetic Progression in portion Arithmetic Progressions of Mathematics – Class 10

The n^th term if an AP is 5n + 2, then the sum of first n terms of the

1.	The n^th term if an AP is 5n + 2, then the sum of first n terms of the AP will be __________(a) \(\frac {n^2 – 8}{2}\)(b) \(\frac {n^2 + 8}{2}\)(c) \(\frac {n^2 – 9}{2}\)(d) \(\frac {n^2 + 9}{2}\)I got this question during an internship interview.The question is from Sum of N Terms of Arithmetic Progression in portion Arithmetic Progressions of Mathematics – Class 10
Answer» Correct ANSWER is (d) \(\FRAC {n^2 + 9}{2}\) Explanation: n^th term = 5n + 2 Tn = 5n + 2 a = T1 = 5(1) + 2 = 7 d = T2 – T1 = 5(2) + 2 – (5 + 2) = 5 We KNOW that, Sn = \(\frac {n}{2}\) (2a + (n – 1)d) Sn = \(\frac {n}{2}\) (2(7) + (n – 1)5) Sn = 7n + \(\frac {n^2}{2} – \frac {5n}{2} = \frac {n^2 + 9}{2}\)

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