Jump to content
BrainDen.com - Brain Teasers
  • 0

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?

Link to post
Share on other sites

4 answers to this question

Recommended Posts

  • 0
  • 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!
Link to post
Share on other sites
  • 0

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
Link to post
Share on other sites
  • 0

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.
Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...