Question

How do you find the nth term rule for `-3,12,-48,192,...`?

Answer 1

`t_n=3/4(-4)^n`.

Explanation:

Let us denote, by `t_n`, the `n^(th)` term of the seq.

We find that, `t_2/t_1=-4, t_3/t_2=-4, t_4/t_3=-4,...`

We conclude that the given seq. is a Geometric Seq., with,

`t_1=-3, "&, common ratio r=-4"`

The Formula for the General Term `t_n` for a Geo. Seq. is,

`t_n=t_1*r^(n-1)=-3*(-4)^(n-1)=3/4(-4)^n`.

Enjoy Maths.!