**Find the sixteenth term of a fibonacci sequence whose first 2 terms are -3 and 9**

Guest Mar 11, 2019

#1**+1 **

Let the first term = a1 and the second term = a2

Note that the 3rd term is = a1 + a2

And the 4th term is = a1 + 2a2

And the 5th term is = 2a1 + 3a2

So....the normal Fibonacci Series is

Fib (n) 1 2 3 4 5

Term 1 1 2 3 5 etc

Then...in the above series....it appears that the nth term (after the second one ) is given by :

Fib (n -2 )*a1 + Fib (n - 1)*a2

So....the 16th term is

Fib (16 - 2) * a1 + Fib (16 - 1) * a2 =

FIb (14) *( -3) + Fib (15) * 9

Note..... Fib (11) = 89 Fib (12) = 144 Fib (13) = 233 Fib (14) = 377 Fib(15) = 610

So....the 16th term is

(377)* (-3) + 610 * 9 =

4359

CPhill Mar 11, 2019