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Permutations And Combinations
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
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