Question

Which term of the series:

21, 18, 15 ....... is –81? 

Can any term of this series be zero? If yes, find the number of terms.

Answer 1

The given A.P. is 21, 18, 15, .......

Here, first term a = 21 and common difference d = 18 – 21 = 3

Let n^th term of the given A.P. be –81

`=>` –81 = a + (n – 1)d

`=>` –81 = 21 + (n – 1) × (–3)

`=>` –102 = (n – 1) × (–3)

`=>` n – 1 = 34

`=>` n = 35

Thus, the 35^th term of the given A.P. is –81.

Let p^th term of this A.P. be 0

`=>` 21 + (p – 1) × (–3) = 0

`=>` 21 – 3p + 3 = 0

`=>` p = 8

Thus, 8^th term of this A.P. is 0