For example,
if I want to find the 15th term of the Fibonacci sequence,
how can I solve it by a faster way?
2007-06-04 01:03:21 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Use Binet's formula.
2007-06-04 01:10:46 · answer #1 · answered by Anonymous · 0⤊ 0⤋
There are (literally) hundreds of sites on the net which have tons of 'canonical form' expressions for Fibonacci (and related) series. Just type 'Fibonacci Series' into any good search engine and start looking.
Most of the cannonical forms I've ever seen for Fibonacci have been for sums of terms, or they're given in terms of some related series. Very few of them are much less computationally intense that the direct solution. If you have a programmable calculator, write a short program.
Doug
2007-06-04 01:11:57 · answer #2 · answered by doug_donaghue 7 · 0⤊ 0⤋
The Fibonacci sequence is a million, a million, 2, 3, 5, 8, ... the place each and each term is the sum of the two previous words, so what you have could be a Fibonacci-like sequence. the subsequent term on your sequence is 29 + 40 seven = seventy six
2016-11-25 21:16:03 · answer #3 · answered by waltman 3 · 0⤊ 0⤋
Write a computer script. Solving Fibonacci sequences is a great task for a recursive algorithm. I recommend Python.
2007-06-04 01:10:03 · answer #4 · answered by poorcocoboiboi 6 · 1⤊ 0⤋
There is that formula involving the Golden Ratio mentioned by a few other posters, but, if you are doing this by hand, it is hardly faster. ("Let's see... what is (√5 + 1)/2 to the 15th power...") Sorry, but just adding successive terms is the fastest way to get your number by hand.
2007-06-04 01:42:43 · answer #5 · answered by Anonymous · 0⤊ 0⤋
there is a approximate formula to find Fn.
let a = (sqr(5)+1)/2 and b = (sqr(5)-1)/2.
then Fn = (a^n + b^n)/sqr(5)
in our case, F15 = (a^15 + b^15)/sqr(5)
The answer is approximately 609.99999999999999999999999999998 (checked with scientific calculator)
a^15 = 1364.000733137435857404797968963
b^15 = 7.3313743585740479796896303925181e-4
the exact answer is 610.
2007-06-04 01:18:45 · answer #6 · answered by veeraa1729 2 · 0⤊ 0⤋
we knw in fibbonici series d 3rd term equals 2 d sum of 1st n 2nd term......
i.e 0,1,1,2,3,5,8,13.........
in general nth term let it b a(n)=a(n-1)+a(n-2)
further whn u solve it u ll com 2 a formula which is
a(n)=[(phi)^n-(-phi)^n]/sqrt(5).....where phi=1.61 and n is d nth term.............
2007-06-04 01:13:22 · answer #7 · answered by abhi_007 1 · 0⤊ 0⤋