phil1882 13 Posted July 15, 2014 Report Share Posted July 15, 2014 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? Quote Link to post Share on other sites

0 Solution nana77 17 Posted July 15, 2014 Solution Report Share Posted July 15, 2014 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! Quote Link to post Share on other sites

0 DeGe 9 Posted July 15, 2014 Report Share Posted July 15, 2014 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 Quote Link to post Share on other sites

0 nana77 17 Posted July 15, 2014 Report Share Posted July 15, 2014 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. Quote Link to post Share on other sites

0 phil1882 13 Posted July 15, 2014 Author Report Share Posted July 15, 2014 nice solve guys. Quote Link to post Share on other sites

## Question

## phil1882 13

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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