How do you write an explicit formula for the sequence ? 640,160,40,10,..

Question

4097 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-26T01:42:59

$a_n=640*(1/4)^(n-1)$

This is a geometric sequence; the ratio of two consecutive terms is the same:

$160/640=1/4$

$40/160=1/4$

$10/40=1/4$

The explicit or general formula of a geometric sequence is

$a_n=a_1*r^(n-1)$ with $a_1$ as the first term, $r$ as the common ratio, and $n$ as the $n^(th)$ term.

Plug in:

$a_n=640*(1/4)^(n-1)$

Double Check:

$a_2=640*(1/4)^(2-1)=640/4=160$