已知数列an是公比为q的等比数列 1.证明a3n为等比数列 并求其公比

1、因为an是等比数列
所以a3n=a1*q^3n-1
a3(n+1）=a1*q^3n-2
即a3(n+1)/a3n=a1*q^3n-2/a1*q^3n-1
=q^-1=1/q
2、an+an+1=a1q^n-1+a1q^n=a1q^n-1*(1+q)
an+1+an+2=a1q^n+aq^n+1=a1q^n*（1+q)
因为q不等于-1也就是1+q不等于0
所以an+1+an+2/an+an+1
=a1q^n*（1+q)/a1q^n-1*(1+q)
=q
所以{an+an+1}是等比数列