Question

证明:等比数列中,若m、n、q∈N,且m+n=2q,则am*an=aq^2

Answer 1

设等比数列的公比为t,

根据等比数列的通项公式：an=a1•t^(n-1),

am= a1•t^(m-1),

aq=a1•t^(q-1).

∴am *an= [a1•t^(m-1)][ a1•t^(n-1)]

= a1^2•t^(m+n-2)

= a1^2•t^(2q-2)

=[ a1•t^(q-1)] ^2

= aq^2.

结论成立.