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# fibinnochi might have been here, 2

Go to solution Solved by nana77,

## Question

given the sequence An = An-1 +An-2

and two numbers in the sequence, along with their place in it; is it always possible to find any An?

if so, what would be the method?

for example, if you knew A15 = 1001 and A7 to be 31, could you solve for A16?

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• Solution

Tricky Phil!

Rewrite s7 and s15 in terms of s1 and s2:

5s1+8s2 = 31
s1=31/5-8s2/5

233s1+377s2 = 1001
s1=1001/233-377s2/233

Take 2 equations for s1 and solve for s2
21s2=2218
s2= -105.6190476
and solve for s1
s1 = 175.1904

Knowing those, s16 = 1619.1908

a non-integer sequence! Tricky tricky!
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Let S1 and S2 be the first 2 terms

Then S3 = S1 + S2
S4 = S1 + 2S2
S5 = 2S1 + 3S2
S6 = 3S1 + 5S2
... and so on

Given any Sn and Sm, you just need to solve 2 equations having 2 variables S1 and S2
You can then find out all the S
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That is brilliant!

So the general rule for the Fibinacci Sequence is itself the Fibinacci Sequence!

And here I was trying to solve a16 in terms of a15 and a7 using substitution (time consuming). Rather than just brute force it which would have been simple. When I should have been looking at the start. Kudos.
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nice solve guys.

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