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

(Q 23B- 30/3/3 – CBSE 2026 Question Paper)

Ans:

Step 1: From the given AP,

First term a = 21

and common difference, d = 18 – 21 = – 3

Step 2: Let’s consider that sum of n terms will give zero.

And, we know that in an AP, Sum of n terms is given by:

S_n = [2a + (n – 1) d]

∴ 0 = [2 (21) + (n – 1) (- 3)] (∵ a = 4, d = – 3)

∴ 0 x 2 = n [42 – 3 (n – 1)]

∴ 0 = n (42 – 3 n + 3)

∴ 0 = n (45 – 3 n)

∴ we get 2 values of n as:

From 1^st factor, n = 0

and from 2^nd factor, 45 – 3n = 0

∴ 3 n = 45

∴ n = = 15

Here, we reject n = 0, because number of terms can not be zero.

and accept n = 15.

Therefore, sum of 15 terms will be 0.

Check: If a = 21, d = – 3 and n = 15
Sum of 15 terms = [2a + (n – 1) d] = [2 (21) + (15 – 1) (- 3)] = (42 – 42) = (0) = 0
Since given condition is matched, our answer is correct.

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