Question

Which term of the A.P. : 65, 61, 57, 53, .............. is the first negative term?

Answer 1

It is given that

AP : 65, 61, 57, 53

First term (a) = 65 and common difference (d) = 61 – 65 = –4

Consider the n^th term of the A.P. as the first negative term

i.e., a_n < 0

We know that n^th term of an AP,

a_n = a + (n – 1)d

Here, [a + (n – 1)d] < 0

Substituting the values

`\implies` 65 + (n – 1) (– 4) < 0

`\implies` 65 – 4n + 4 < 0

`\implies` 69 – 4n < 0

`\implies` 4n > 69

`\implies` `"n" > 69/4`

`\implies` n > 17.25

`\implies` n = 18

So the 18^th term is the first negative term of the given AP.