Question

How many terms in A.P. 18,16,14--------- must be taken so that their sums is zero.
​

Answer 1

Answer:

19 terms must be taken so that the sum is zero

Answer 2

Given:-

• A.P. 18,16,14---------
• Sum = 0

To find:-

• Find the nth term of an Ap.?

Solutions:-

• First term (a) = 18
• Common difference (d) = a2 - a1 = 16 - 18 = -2

• Let the number of terms of an Ap be 'n'

According to the questions;

=> l = a + (n - 1)d

=> l = 18 + (n - 1)(-2)

=> l = 18 - 2n + 2

=> l = 20 - 2n ..........(i)

Sn = n/2[a + l]

=> 0 = n/2 × [18 + 20 - 2n] (using Eq ...(i)....)

=> 0 = n/2 × [38 - 2n]

=> 0 = n/2 × 2[19 - n]

=> 0 = n[19 - n]

=> 0 = 19n - n²

=> n² = 19n

=> n = 19

Hence, the nth terms of an Ap is 19.