What is the formula for the nth term for the example 5, 0.5, 0.05, 0.005, 0.0005, ...?

1 Answer
Feb 4, 2018

# a_n = 5*(1/10)^(n-1) #

Explanation:

This sequence is known as a geometric sequence, where the next term is obtained by multiplying the prior term by a ' common ratio'

The general term for a geometric sequence is:

#a_n = ar^(n-1) #

Where

#a = "first term" #

#r = "common ratio" #

Hence in this case #a = 5 #

To find #r# we need to consider what we multiply #5# by to get #0.5 #

We multiply by #1/10 #

#=> r = 1/10 #

#color(blue)(therefore a_n = 5*(1/10)^(n-1) #