Question

Find four consecutive term in ap such that sum of second and third term is 18&product of first and fourth term is 45

Answer 1

Let the AP be

a-3d, a-d, a+d, a+3d

with first term (a-3d) and common difference 2d

According to the condition of the given problem

(a-3d)(a+3d) = 45

a²-9d² = 45.........(1)

(a-d)+(a+d) = 18

2a = 18

a = 9.......(2)

Substituting (2) in (1)

9²-9d² = 45

9-d² = 5

d² = 4

d = 2 OR d = (-2)

Hence the required AP is

i) 3,7,11,15 OR ii) 15,11,7,3

(Both answers are necessary)