Question

How many terms of the A.P. 3, 5, 7, 9, ... must be added to get the sum 120?

Answer 1

AP = 3, 5, 7, 9, …

Here, a = 3, d = 5 – 3 = 2 and S_n = 120

We know that,

⇒ 120 = n[2+n]

⇒ n² + 2n – 120 = 0

⇒ n² + 12n – 10n – 120 = 0

⇒ n(n + 12) - 10(n + 12) = 0

⇒ (n – 10)(n + 12) = 0

⇒ n – 10 = 0 or n + 12 = 0

⇒ n = 10 or n = -12

But number of terms can’t be negative. So, n = 10

Hence, for n = 10 the sum is 120 for the given AP.