Question

How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?

How many terms of the A.P. 21, 18, 15,... must be added to get the sum zero?

Answer 1

The given AP is 21, 18, 15,……….

Here, a = 21 and d =18 − 21 = − 3

Let the required number of terms be n. Then,

S_n = 0

`⇒ n/2 [ 2 xx 21 + (n − 1) xx (−3) ] = 0`        `...[{s_n = n/2 [  2a +(n − 1) d]}]`

`⇒ n/2 (42 − 3n + 3) = 0`

⇒  n (45 − 3n) = 0

⇒ n = 0 or 45 − 3n = 0

⇒  n = 0 or n = 15

∴ n = 15                  (Number of terms cannot be zero)

Hence, the required number of terms is 15.