# Given the two terms in a geometric sequence how do you find the recursive formula... a1=-4 and a4=-500?

##### 2 Answers

Recursive formula is

#### Explanation:

In a geometric sequence, if

Here

Hence recursive formula is

Recursive formulation:

#{ (a_1 = -4), (a_(n+1) = 5a_n color(white)(000) (n = 1,2,3,...)) :}#

#### Explanation:

We are given:

#{ (a_1 = -4), (a_4 = -500) :}#

The general formula for the

#a_n = a r^(n-1)#

where

A recursive formula can be given as:

#{ (a_1 = a), (a_(n+1) = ra_n color(white)(000) (n = 1,2,3,...)) :}#

In our example:

#5^3 = 125 = (-500)/(-4) = r_4/r_1 = (color(red)(cancel(color(black)(a))) r^(4-1))/(color(red)(cancel(color(black)(a))) r^(1-1)) = r^3#

So the only possible Real value for

**Footnote**

There are two other possibilities for a geometric sequence with

This is because