Question

Term to term rule for:
4,12,36,108,324

Answer 1

It's the geometric sequence with common ratio r = 3.

`a_1=4\\a_2=3a_1\to a_2=3(4)=12\\a_3=3a_2\to a_3=3(12)=36\\a_4=3a_3\to a_4=3(36)=108\\a_5=3a_4\to a_5=3(108)=324\\a_6=3a_5\to a_6=3(324)=972\\\vdots`

The formula of a general term of a geometric sequence:

`a_n=a_1r^(n-1)`

`a_n=4(3)^(n-1)=4(3)^n(3)^(-1)=4(3)^n\left((1)/(3)\right)=(4)/(3)(3)^n`