SOLUTION: What is equation for sequence 1, 1, 1/2, 1/3, 1/4, 1/9...

Algebra.Com
Question 838454: What is equation for sequence 1, 1, 1/2, 1/3, 1/4, 1/9...
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
1/1, 1/1, 1/2, 1/3, 1/4, 1/9...

Sequence of denominators bn: 1,1,2,3,4,9,...

5(b3)-6(b1) = 5(2)-6(1) = 10-6 = 4 = b5

5(b4)-6(b2) = 5(3)-6(1) = 15-6 = 9 = b6

So a recursion equation for the sequence of denominators is:

b1=1,b2=1,b3=2,bn=5bn-2-6bn-4

Therefore a recursion equation for the given sequence an is

a1=1,a2=1,a3=1/2,an=5/an-2-6/an-4    

Edwin
RELATED QUESTIONS

What algebraic expression best describes the sequence 1, 1/2, 1/3, 1/4,... (answered by Fombitz)
What is the arithmetic sequence of 1, 1/4, 1/9,... (answered by richard1234)
What is the general term of the arithmetic sequence:... (answered by MathLover1)
Tell whether the sequence is arithmetic. If it is, what is the common difference? 1, 1 (answered by rfer)
write a recursive rule for the sequence 1, 1/2, 1/2, 3/4, 3/2,... (answered by Edwin McCravy)
what is 4 1/2 - 1/6 = 1... (answered by stanbon)
what is 1 1/2 + 3/8 +1... (answered by Alan3354,Ryan K)
What are the next 3 numbers in the sequence. 1/4, 0, -1/4,... (answered by robertb)
guess a simple formula for the sequence hat begin: -1, 1/2, -1/3, 1/4,... (answered by josmiceli)