Given A.P: 121, 117, 113, ……
a = 121 and d = a2 – a1
= 117 – 121 = -4
Let the nth term be the first negative term of the given G.P.
Then, an < 0
⇒ an = a + (n – 1) d < 0
⇒ 121 + (n – 1) (-4) < 0
⇒ 121 – 4n + 4 < 0
⇒ 125 – 4n < 0
⇒ -4n < -125
⇒ 4n >125
⇒ n > 125/4
n > 31.25
∴ When n = 32, the term becomes negative, (or) 32 nd term is the first negative term of the given A.P.