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

1 Answer
Feb 26, 2018

a_n=640*(1/4)^(n-1)an=640(14)n1

Explanation:

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

160/640=1/4160640=14

40/160=1/440160=14

10/40=1/41040=14

The explicit or general formula of a geometric sequence is

a_n=a_1*r^(n-1)an=a1rn1 with a_1a1 as the first term, rr as the common ratio, and nn as the n^(th)nth term.

Plug in:

a_n=640*(1/4)^(n-1)an=640(14)n1

Double Check:

a_2=640*(1/4)^(2-1)=640/4=160a2=640(14)21=6404=160