Question

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 1

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 + \(\frac {n^2}{2} – \frac {5n}{2} = \frac {n^2 + 9}{2}\)