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

Here, first term = a = 21

Common difference = d = 18 - 21 = - 3

Let first n terms of the AP sums to zero.

∴ S_n = 0

To find: n

Now, S_n = (n/2) × [2a + (n - 1)d]

Since, S_n = 0

∴ (n/2) × [2a + (n - 1)d] = 0

⇒ (n/2) × [2(21) + (n - 1)(-3)] = 0

⇒ (n/2) × [42 - 3n + 3)] = 0

⇒ (n/2) × [45 - 3n] = 0

⇒ [45 - 3n] = 0

⇒ 45 = 3n

⇒ n = 15

∴ 15 terms of the given AP sums to zero.