Permutations and Combinations

Permutations and Combinations

Question

Show that products of the corresponding terms of sequences a, ar, ar2, .........ar n – 1 and A, AR, AR2, ........ An – 1 form a GP. and find common ratio.

Answer

If we multiply corresponding terms of given two sequences.
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Here,              straight t subscript straight n over straight t subscript straight n minus 1 end subscript space equals space fraction numerator ar to the power of straight n minus 1 end exponent. space AR to the power of straight n minus 1 end exponent over denominator ar to the power of straight n minus 2 end exponent. AR to the power of straight n minus 2 end exponent end fraction space equals space straight r. space straight R space equals space constant

∴  Above sequence is a G.P. with common ratio r . R.


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