Question

Which term of the AP 24, 21, 18, 15, ………. is the first negative term?

Answer 1

Given,

AP is 24, 21, 18, 15, …… 

First term of AP is a = 24. 

Common difference of AP is d = a₂ − a₁ 

= 21 − 24 = −3. 

Since,

First term is 24 which is multiple of 3 and common difference is – 3. 

Therefore, 

All terms of AP are multiple of 3. 

∴ First negative term of given AP is – 3. 

Let n^th term of AP is – 3. 

∴ a + (n − 1)d = −3 

(∵ n th term of AP is given by an = a + (n − 1)d) 

⇒ 24 + (n − 1) × −3 = −3 

(∵ a = 24 & d = −3) 

⇒ −3(n − 1) 

= −3 − 24 

= −27

⇒ n −1 = \(\frac{-27}{-3}\) = 9

⇒ n = 1 + 9 = 10.

Hence,

10th term of given AP is the first negative term.