Question

For the following geometric sequence, find the recursive formula.

Answer 1

Answer:

$a_{n}=-\frac{1}{4}(a_{n-1})$

Step-by-step explanation:

To find recursive formula in a geometric sequence, you need to first find the common ratio, 'r', between the numbers in the given data set.  From the data set given, it appears that the previous number is multiplied by $-\frac{1}{4}$ so, r = $-\frac{1}{4}$.

Recursive formula involves two other variables:

$a_{n}=$ the $n^{th}$ term in the sequence

$a_{n-1}$=the term before the $n^{th}$ term

So, the final formula is:  $a_{n}=-\frac{1}{4}(a_{n-1})$