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in Arithmetic Progression by (36.5k points)
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Which term of the AP: 121, 117, 113,…, is the first negative term? [Find n for an < 0]

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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.

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