Question

The values in the table represent an exponential function. What is the

common ratio of the associated geometric sequence?
х
у
7
1
2
21
3
4
63
189
567
LO

Answer 1

The common ratio is 3

Explanation:

Recall that an exponential function is defined as:

`f(x)=A\,r^x`

where A is a multiplicative factor normally associated with the "first term of a geometric sequence", and "r" is the "common ratio" that is used to generate each of the terms of the associated geometric sequence:

`a_n=a_1*r^(n-1)`

So in this case:

`a_1=7=a_1\,r^0`

`a_2=21=a_1\,r^1=7\,r`

from which we derive that the common ratio "r" must be "3".

we can also corroborate that this is in fact the correct common ratio by testing the following terms of the sequence;

`a_3=63=7\,r^2=7\,*\,9`

`a_4=189=7\,r^3=7\,*\,27`

`a_5=567=7\,r^4=7\,*\,81`