Question

How do you find the explicit formula for the following sequence 0.2, -0.06, 0.018, -0.0054, 0.00162 ...?

Answer 1

General Term `t_n=0.2(-0.3)^(n-1).`

Explanation:

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

Then, we find that, `t_2/t_1=-0.06/0.2=-0.3`
`t_3/t_2= -0.0.018/-0.06=-0.3`
`t_4/t_3-0.0054/0.018=-0.3,` & so on.

We conclude the it is a Geometric Seq. with first term `= t_1=a=0.2` and common ratio `=r=-0.3`

Its General Term is given by the formula `=t_n=a*r^(n-1),` i.e.,
`t_n=0.2(-0.3)^(n-1).`