Question

Four numbers are in arithmetic progression. The sum of first and last terms is 8 and the product of both middle terms is 15. The least number of the series is

(A)  4 

(B)  3 

(C)  2 

(D)  1

Answer 1

Correct option (D) 1

Let A₁,A₂,A₃ and A₄ be four numbers in AP.

A₁ + A₄ = 8  ....(1)

and A₂ .A₃ = 15 ...(2)

The sum of terms equidistant from the beginning and end is constant and is equal to sum of first and last terms. Hence

A₂ + A₃ = A₁ + A₄ = 8 ....(3)

From Eqs. (2) and (3),

Hence, the series is 1, 3, 5, 7.

So that the least number in the series is 1.