Question

Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.

Answer 1

Let 0 be the n^th term of given AP i.e., a_n = 0.

Given that, first term a = 31

Common difference, d = 28 – 31 = – 3

The n^th terms of an AP, is

`a_n = a + (n - 1)d`

⇒ 0 = `31 + (n - 1)(-3)`

⇒ `3(n - 1)` = 31

⇒ `n - 1 = 31/3`

∴ `n = 31/3 + 1`

= `34/3`

= `11 1/3`

Since, n should be positive integer.

So, 0 is not a term of the given AP.