Question

Let a₁, a₂, a₃, a₄ be in A.P. If a₁ + a₄ = 10 and a₂a₃ = 24, then the least term of them is

(a) 1 

(b) 2 

(c) 3 

(d) 4

Answer 1

Answer : (b) 2

Let a₁ = a – 3d, a₂ = a – d, a₃ = a + d, a₄ = a + 3d 

Given, 

a₁ + a₄ = 10 ⇒ a – 3d + a + 3d = 10 

⇒ 2a = 10 ⇒ a = 5 

Also, a₂ a₃ = 24 ⇒ (a – d) (a + d) = 24 

⇒ a² – d² = 24 

⇒ 25 – d² = 24 

⇒ d² = 1 

⇒ d = 1 

∴ The least term is a – 3d 

= 5 – 3 = 2.