If {a_{n}} and {b_{n}} are geometric sequences with common ratios of r₁ and r₂, is {a_{n}b_{n}} a geometric sequence too? If yes, what is the common ratio?

Question

Mathematics

Phoenix Lynn

8 October, 16:10

If {a_{n}} and {b_{n}} are geometric sequences with common ratios of r₁ and r₂, is {a_{n}b_{n}} a geometric sequence too? If yes, what is the common ratio?

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Answers (1)

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Billy Braun · Answer 1

A_{n+1}b_{n+1} / a_{n}b_{n} = (a_{n+1} / a_{n}) * (b_{n+1} / b_{n}) = (r1) * (r2) = >

{a_{n}b_{n}} a geometric sequence; the common ratio is (r1) * (r2).