Show that the products of the corresponding terms of the sequence `a,ar, ar^(2),… ar^(n-1)` and `A,AR, AR^(2),…AR^(n-1)` from a G.P. and find the common ratio.

Answer

N/a

Explanation

First sequence : `a,ar,ar^(2),…ar^(n-1)`
Second sequence `:A,AR,AR^(2),…. AR^(n-1)`
Sequence formed by the product of corresponding term of two sequences.
`aA,aArR,aAr^(2)R^(2),…aAr^(n-1)R^(n-1)`
`-=aA,aA(rR),aA(rR),….,aA(rR)^(n-1)`
Here `(a_(2))/(a_(1))=(a_(3))/(a_(2))=rR`
Therefore, this sequence is a G.P and its common ratio is rR.
`:. " Common ratio"=rR`