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Permutations And Combinations
Find four numbers in A.P. whose sum is 32 and the product of extremes is to the product of means is 7 : 15.
Let the four number in A.P. be a  3d, a  d, a + d, a + 3d.
Since the sum of four numbers = 32
∴ a  3d + a  d + a + d + a + 3d = 32
or 4a = 32 or a = 8
Since the ratio of the product of extremes to the product of means is 7:15.
∴ or
or or
or or
or or
When d = 2 and a = 8 numbers are 8  3(2), 8  2, 8 + 2, 8 + 3(2)
2, 6, 10, 14
When d = 2 and a = 8 numbers are 8  3(2), 8  (2), 8 + (2), 8 + 3(2)
14, 10, 6, 2
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