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

 Mar 11, 2019
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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

 

 

cool cool cool

 Mar 11, 2019

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