Question

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 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) .