Question

Write a recursive formula for 72,12,2

Answer 1

First you need to find out if the set  is an arithmetic sequence or  a geometric sequence.

Is it Arithmetic?
To find out if the set is arithmetic, the set has to have a common deference. You check for a common difference by taking the consecutive number and subtracting the number that comes before it. So
12 - 72 = -60
2 - 12 = -10
The numbers are not the same so there is no common difference. So the set is not arithmetic.

Is it Geometric?
To find out, you need to see if there is a common ratio between the numbers.
Take the consecutive number 12 and divide it by 72 and so on.
12/72 = .1666666667 = $\frac{1}{6}$
2/12 =   .1666666667 = $\frac{1}{6}$

They are the same so the set is geometric.

Now that you know the set is geometric, it is time to write a recursive formula for 72,12,2
To write this formula, you need to state the first term and use the common ratio that was found, which is $\frac{1}{6}$

State the first term:
$a_1 = 72$

State the Relationship
$a_n = \frac{1}{6}a_{n-1}$

All together now!
$a_1 = 72; a_n = \frac{1}{6}a_{n-1}$