設(shè)等比數(shù)列的通項為an,公比為q,則有an=a(n-1)*q
將an分成三個三個一組,得到n/3組
每組三個乘積設(shè)為bn=a(3n-2)*a(3n-1)*a3n,則b1=a1*a2*a3=2,b(n/3)=a(n-2)*a(n-1)*an=4
又由bn/b(n-1)=a(3n-2)*a(3n-1)*a3n/a(3n-5)*a(3n-4)*a(3n-3)=q^9
所以bn也為等比數(shù)列,設(shè)公比為k
所以bn為以2為首項,4為尾項,共有x項(x=n/3),乘積為64的等比數(shù)列
由b(x)/b1=k^(x-1)=2
所有項乘積為 b1*b2*...*bx=2^x*k^[x(x-1)/2]=64
將k^(x-1)=2代入得
2^(3x/2)=64
解得x=9
所以n=3x=27