## Question

###### How do you use the geometric sequence formula to find the nth term?

How do you use the geometric sequence formula to find the nth term?

## Answers

A geometric sequence is always of the form

#t_n=t_"n-1"*r# Every next term is

#r# times as large as the one before.So starting with

#t_0# (the "start term") we get:

#t_1=r*t_0#

#t_2=r*t_1=r*r*t_0=r^2*t_0#

......

#t_n=r^n*t_0# Answer:

#t_n=r^n*t_0#

#t_0# being the start term,#r# being the ratio

Extra:

If#r>1# then the sequence is said to beincreasing

if#r=1# then all numbers in the sequence are the same

If#r<1# then the sequence is said to bedecreasing,

and a total sum may be calculated for an infinite sequence:

sum#sum=t_0/(1-r)#

Example:

The sequence#1,1/2,1/4,1/8...#

Here the#t_0=1# and the ratio#r=1/2#

Total sum of this infinite sequence:

#sum=t_0/(1-r)=1/(1-1/2)=2#

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