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)`