100th term of sequence?

X

xc630

Junior Member
Joined
Sep 1, 2005
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164
Hi I was asked to give the 1st eight terms of the equences defined recursively by t1=4, t2=8 and Tn= tn-1/tn-2

I found the terms to be 4,8,2,1/4,1/8,1/2,4, and 8

They then asked me to find the 100th term but I am having trouble coming up with a formula. I'd appreciate osome help with that. Thanks for your help in advance.
 
LOOk at the pattern of the sequence and THINK ...

4, 8, 2, 1/4, 1/8, 1/2, 4, 8, 2, 1/4, 1/8, 1/2, ...
 
ok i see 4, 8 ,2 and then the same numbers under 1 in fraction form, then it seems to start again. But how would I write this in a formula
 
you don't need a formula. the pattern in the sequence does repeat.

here's another BIG hint ... the 96th term is 1/2.

can you figure out the 100th term now?
 
well, you're half right ...

6th term = 1/2
12th term = 1/2
18th term = 1/2
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(multiples of 6, correct?)
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96th term = 1/2
97th term = 4
98th term = 8
99th term = 2
100th term = 1/4
 
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