Question

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

How many terms of the sequence 18, 16, 14, ... should be taken so that their sum is zero?

Answer 1

The given AP is 18, 16, 14, ...

The first term of the AP = 18

Common difference = 16 − 18 = −2

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

Sum of the first x terms =`x/2`[2×18+(x−1)(−2)]=0

⇒`x/2`[36+(−2x+2)]=0

⇒x(36−2x+2)=0

⇒x(38−2x)=0

Now, either x = 0 or 38 − 2x = 0

But the number of terms cannot be 0.

∴ 38 − 2x = 0

⇒ 38 = 2x

⇒ x = 19

Thus, the sum of the first 19 terms of the AP is 0.