Question

What is the explicit formula for this geometric sequence?

8, 4, 2, 1, …

Answer 1

`a_(n) = (8)/(2^(n-1) )`

Explanation:

A geometric sequence has a constant ratio (r) and is defined by:

`a_n=a_1r^(n-1)`

Since the first value is 8,
`a_(1)` = 8.

`a_n=8r^(n-1)`

We can also see that a_n is double that of the next value in the sequence
`(a_(n) = 2a_(n+1)})`, hence r = 1/2

`a_n=8\left((1)/(2)\right)^(n-1)` or

`a_(n) = (8)/(2^(n-1) )`