Question

Find three numbers in A.P. whose sum is 24 and whose product is 440.

Answer 1

Let the three numbers in A.P. be a – d, a and a + d. 

∴ (a – d) + a + (a + d) = 24

`=>` 3a = 24

`=>` a = 8  ...(1)

Also, (a – d) × a × (a + d) = 440

`=>` (a² – d²) × a = 440

`=>` (8² – d²) × 8 = 440  ...[From (1)]

`=>` 64 – d² = 55

`=>` d² = 9

`=>` d = ±3

When a = 8 and d = 3

Required terms = a – d, a and a + d

= 8 – 3, 8, 8 + 3

= 5, 8, 11

When a = 8 and d = –3

Required term = a – d, a and a + d

= 8 – (–3), 8, 8 + (–3)

= 11, 8, 5