Help with Explicit Sequence Formula

May 2010
2
0
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.
 
Jan 2008
588
242
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 2010
2
0
I figured it out.

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

N = the Sequence number (1, 2, 3, 4, etc.)
 
Feb 2010
1,036
386
Dirty South
\(\displaystyle a_n = 4^{3-n}\)

for n = 1,2,....