Question

How many terms of the sequence should be taken so that their sum is zero?

Answer 1

19 terms of the AP will sum to zero.

Step-by-step explanation:

The question is incomplete. The complete question is "How many terms of AP 18,16,14... is to be taken so that their sum is zero?"

Given: AP 18,16,14...  

Find: n where sum of AP is zero.

Solution:

Sum of AP = n/2 (2a + (n-1)d)

   0 = n/2 (2*18 +(n-1)(-2))

   0 = n/2 (36 - 2n + 2)

   0 = n (38 - 2n)

   0 = 38n - 2n2

   0 = 2n (19 - n)

Therefore n = 19.

19 terms of the AP will sum to zero.