Question

How many terms of the AP 5,10,15,20….. must be added to get a sum of 330?

(a) -11

(b) -12

(c) 12

(d) 11

The question was asked in final exam.

My question is based upon Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right option is (d) 11

Explanation: Here a = 5, d = 5 and Sn = 330

We know that, Sn = \(\frac {n}{2}\) (2a + (n – 1)d)

330 = \(\frac {n}{2}\) (2(5) + (n – 1)5)

330 = \(\frac {n}{2}\) (10 + 5n – 5)

330 = \(\frac {n}{2}\) (5 + 5n)

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

660 = 5n^2 + 5n

n^2 + n – 132 = 0

n = -12, 11

Since, n cannot be negative

Hence value of n is 11.