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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?



Answer :

crisforp
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) .

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