Question

Write a recursive and explicit rule for each geometric sequence, and then find the next 3 terms.

1.) 2, 8, 32


2.) 1004, 512, 256

Answer 1

Hello,

1)
$a_{0}=2$
$a_{1}=a_{0}*4=8$
$a_{2}=a_{1}*4=a_{0}*4^2=32$
$a_{3}=a_{2}*4=a_{0}*4^3=128$
$a_{4}=a_{3}*4=a_{0}*4^4=512$
$a_{5}=a_{4}*4=a_{0}*4^5=2048$
...
$a_{n+1}=a_{n}*4=a_{0}*4^{n+1}$


2)
$a_{0}=1024$
$a_{1}=a_{0}*0.5=512$
$a_{2}=a_{1}*0.5=a_{0}*0.5^{2}=256$
$a_{3}=a_{2}*0.5=a_{0}*0.5^{3}=128$
$a_{4}=a_{3}*0.5=a_{0}*0.5^{4}=64$
$a_{5}=a_{4}*0.5=a_{0}*0.5^{5}=32$
....
$a_{n+1}=a_{n}*0.5=a_{0}*0.5^{n+1}$