if f(n+2)=2f(n)+f(n+1) and f(1)=1 and f(2)=1 , what is f(8)-f(7) ?

usagirl007A

usagirl007A

Answered question

2021-03-12

if f(n+2)=2f(n)+f(n+1) and f(1)=1 and f(2)=1 , what is f(8)f(7) ?

Answer & Explanation

Mitchel Aguirre

Mitchel Aguirre

Skilled2021-03-13Added 94 answers

Given that f(n+2)=2f(n)+f(n+1) with f(1)=1 and f(2)=1. Start with putting n=6 in the above we have f(8)f(7)=2f(6)
=2(2f(4)+f(5))

=2(2f(4)+2f(3)+f(4)) 

=2(3f(4)+2f(3)) 

=2(3f(2f(2)+f(3))+2f(3))

=2(6f(2)+3f(3)+2f(3))

=2(6f(2)+5f(3))

=2(6f(2)+5(2f(1)+f(2)))

=2(6f(2)+10f(1)+5f(2))

=2(11f(2)+10f(1))

=2(11+10)=221 =42

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