Question

How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?

Answer 1

 The given AP is 65, 60, 55, ...

First term of the AP = 65

Common difference = 60 − 65 = −5

Let the sum of the first x terms of the AP be 0.

Sum of first x terms =`x/2`[2×65+(x−1)(−5)]=0

⇒`x/2`[130+(−5x+5)]=0

⇒x(130−5x+5)=0

⇒x(135−5x)=0

Now, either x = 0 or 135 − 5x = 0.

Since the number of terms cannot be 0, x≠0.

∴ 135 − 5x = 0

⇒ 135 = 5x

⇒ x = 27

Thus, the sum of the first 27 terms of the AP is 0.