等差数列｛an｝的公差为d且a7＝4,a19＝2a9.数列bn为等比数列,且b2＝2,b5＝16（1）求an,bn的通项公式

Question

等差数列｛an｝的公差为d且a7＝4,a19＝2a9.数列bn为等比数列,且b2＝2,b5＝16
（1）求an,bn的通项公式

Answer 1

an=a1+(n-1)d
a7 = 4
a1+6d = 4 (1)
a19=2a9
a1+18d= 2(a1+8d)
a1-2d =0 (2)
(1) -(2)
8d =4
d =1/2
from (1) => a1=1
an = 1+(1/2)(n-1) =(1/2)(n+1)
bn = b1.q^(n-1)
b2 = b1q =2 (3)
b5= b1.q^4=16 (4)
(4)/(3)
q^3=8
q=2
from (3) => b1= 1
bn = 2^(n-1)