# Help with Explicit Sequence Formula

• May 24th 2010, 05:16 PM
bfbcool2
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 \$\displaystyle a_n = 1/4a_n-1\$, but I don't know how to make an explicit formula.
• May 24th 2010, 05:25 PM
Gusbob
Quote:

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 \$\displaystyle 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:

\$\displaystyle 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.
• May 24th 2010, 07:30 PM
bfbcool2
I figured it out.

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

N = the Sequence number (1, 2, 3, 4, etc.)
• May 24th 2010, 07:33 PM
harish21
\$\displaystyle a_n = 4^{3-n}\$

for n = 1,2,....