Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 4, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______
Numerical Answers Expected!

Answer 1

Try plugging in 5 into f(n):
\[f(5)=f(1)+f(2)+f(5−1)=2+4+f(4)=6+f(4)\]

what is f(4)? use the rule again
\[ f(4)=f(1)+f(2)+f(4−1)=2+4+f(3)=6+f(3)\]

And then
\[f(3)=f(1)+f(2)+f(3−1)=2+4+f(2)=6+4=10\]

So you now know f(3)'s value. You can go back to f(4) and find its value, and then go back to f(5) and find its value since you'll know f(4)