Question

How do you find the explicit formula for the following sequence 5, 0.5, 0.05, 0.005 ...?

Answer 1

`(x_n)=5*(1/10)^(n-1)` , `n in NN`

Explanation:

This is a geometric sequence with common ratio `r=x_(n+1)/x_n=1/10`.

The first term is `a=5`.

Hence the general term is `(x_n)=ar^(n-1)` , `n in NN`.

`=5*(1/10)^(n-1)`