Question

Find four consecutive term in anA.P such that the sum of second and third terms is 18 and the product of the first and fourth terms is 45

Answer 1

d = 1

a2 + a3 = 18

a + d + a + 2d = 18

2a + 3d = 18

2a = 18-3d

a = 18 - 3d/2................. eq 1

a = 18-3*1/2

a = 15/2

a2 = a + d = 15/2 + 1 = 17/2

a3 = a + 2d = 15/2 + 2*1 = 19/2

a4 = a + 3d = 15/2 + 3*1 = 21/2

Hence the A.p is 15/2, 17/2, 19/2, 21,2......