Question

Which term of the A.P. 121, 117, 113, ... is its first negative term?

[Hint: Find n for a_n < 0]

Answer 1

Given A.P. is 121, 117, 113, ...

a = 121

d = 117 – 121

d = –4

a_n = a + (n – 1) d

= 121 + (n – 1) (–4)

= 121 – 4n + 4

= 125 – 4n

We have to find the first negative term of this A.P.

Therefore, a_n < 0

125 – 4n < 0

125 < 4n

`n > 125/4`

n > 31.25

Therefore, 32^nd term will be the first negative term of this A.P.