Question

Consider the sequence below.

-11, 22, -44, 88, …
Complete the recursively defined function to describe this sequence.
f(0) = ___
f(n) = f(n - 1) · ___ for n = 1, 2, 3, …

Answer 1

Answer: f(0)=11/2

f(n) = f(n - 1) · (-2)

Explanation:

f(0)=f(1)*(f(0+1)/f(1+1))

f(0)=f(1)*(f(1)/f(2))

f(0)=-11*(-11/22)

f(0)=-11*(-1/2) ==> -11/22 simplifies to -1/2

f(0)=-11*(-1)/2

f(0)=11/2

f(n) = f(n - 1) · f(2)/f(2-1)

f(n) = f(n - 1) · f(2)/f(1)

f(n) = f(n - 1) · 22/(-11)

f(n) = f(n - 1) · 2/(-1)

f(n) = f(n - 1) · (-2)