# Math Help - Help with Explicit Sequence Formula

1. ## Help with Explicit Sequence Formula

Write a possible explicit rule for each sequence, and find the 10th term.

16, 4, 1, 1/4, 1/16

I know that the recursive formula is $a_n = 1/4a_n-1$, but I don't know how to make an explicit formula.

2. Originally Posted by bfbcool2
Write a possible explicit rule for each sequence, and find the 10th term.

16, 4, 1, 1/4, 1/16

I know that the recursive formula is $a_n = 1/4a_n-1$, but I don't know how to make an explicit formula.
A term in a geometric series is given by:

$T_n = ar^{n-1}$ where a is the first term, and r is the ratio between any two consecutive terms. You have already found the ratio in your recursive formula.

3. I figured it out.

The formula is $A_n = 1/4^(n-1) +16$

N = the Sequence number (1, 2, 3, 4, etc.)

4. $a_n = 4^{3-n}$

for n = 1,2,....