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.