Permutations and Combinations

Question

Answer

Let a - d, a, a + d be three numbers in A.P. Since their sum is 21

∴ a - d + a + a + d = 21

3a = 21 a = 7

∴ Numbers are 7 - d, 7, 7 + d

It is given that if the second number is reduced by 1 and third is increased by 1 then resulting three numbers form G.P.

∴ 7 - d, 7 - 1, 7 + d + 1 are in G.P. or 7 - d, 6, 8 + d are in G.P.

(8 + d) (7 - d) = 36

56 - 8d + 7d - d^{2} = 36

d =

When a = 7 and d = 4, numbers are 7 - 4, 7 + 4 or 3, 7, 11

when a = 7 and d = -5, numbers are 7 - (-5), 7, 7 - 5 or 12, 7, 2