数列an中a2=3a5=31又数列[1/(an)+1]是等比数列则数列通项an=?

Question

数列an中 a2=3 a5=31 又数列[1/(an)+1]是等比数列 则数列通项an=?

Answer 1

1/(a2+1)=1/4
1/(a5+1)=1/32
q^3=[1/(a5+1)]/[1/(a2+1)]=1/8、q=1/2.
1/(a1+1)=[1/(a2+1)]/q=2*4=8.
{1/(an+1)}是首项为8、公比为1/2的等比数列.
1/(an+1)=8*(1/2)^(n-1)=(1/2)^(n-4).