# How do you find a formula for the nth term of the geometric sequence: 500, 100, 20, 4, ...?

##### 1 Answer

Apr 29, 2016

#### Explanation:

Recall that the formula for the

#color(blue)(|bar(ul(color(white)(a/a)t_n=ar^(n-1)color(white)(a/a)|)))# where:

#t_n=# term number

#a=# first term

#r=# common ratio

#n=# number of terms

Start by determining the value of

Use

#t_n=ar^(n-1)#

#100=500r^(2-1)#

Solve for

#r=1/5#

Now that you have the value of

#color(green)(|bar(ul(color(white)(a/a)t_n=a(1/5)^(n-1)color(white)(a/a)|)))#