Question

Sum of 4 numbers in an ap is 40 and product of their extreme is 91

Answer 1

Sum of 4 numbers in an ap is 40 and product of their extreme is 91

Let the numbers be:

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

From given, we have,         (Sum of 4 numbers in an ap is 40)

a-3d + a-d + a+d + a+3d  = 40

4a = 40

∴ a = 10

From given, we have,           (product of their extreme is 91)

(a-3d) × (a+3d) = 91

a^2-(3d)^2 = 91

10^2 - 9d^2 = 91

100 - 9d^2 = 91

100-91 = 9d^2

9 = 9d^2

∴ d = ± 1

when a = 10  and d = -1

the numbers are: 13, 11, 9, 7

when a = 10  and d = 1

the numbers are:  7, 9, 11, 13