B bfbcool2 May 2010 2 0 May 24, 2010 #1 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.

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.

G Gusbob Jan 2008 588 242 May 24, 2010 #2 bfbcool2 said: 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. Click to expand... 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.

bfbcool2 said: 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. Click to expand... 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.

B bfbcool2 May 2010 2 0 May 24, 2010 #3 I figured it out. The formula is \(\displaystyle A_n = 1/4^(n-1) +16\) N = the Sequence number (1, 2, 3, 4, etc.)

I figured it out. The formula is \(\displaystyle A_n = 1/4^(n-1) +16\) N = the Sequence number (1, 2, 3, 4, etc.)

harish21 Feb 2010 1,036 386 Dirty South May 24, 2010 #4 \(\displaystyle a_n = 4^{3-n}\) for n = 1,2,....