Permutations and Combinations

Permutations and Combinations

Question

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.

Answer

Since K + 2, 4K - 6 and 3K - 2 are three consecutive terms of an A.P.

∴  (4K - 6) - (K + 2) = (3K - 2) - (4K - 6)
or         4K - 6 - K - 2 = 3K - 2 - 4K + 6    or   3K - 8 = -K + 4
or                                        4K =  12              or               K = 3

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