Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Answer 1

7

Answer 2

So we have the conditions:
\[\eqalign{
&f(1)=2 \\
&f(2)=3 \\
&f(n)=f(1)+f(2)+f(n-1); n\gt2 \\
}\]
We can simplify \(f(n)\) to:
\[f(n)=5+f(n-1)\]
So therefore:
\[\eqalign{
f(5)&=5+f(5-1) \\
&=5+f(4) \\
&=5+\big[5+f(3)\big] \\
&=5+\Big[ 5+\big(5+f(2)\big)\Big] \\
&=5+5+5+3 \\
&=18
}\]

Answer 3

So f(5) = 18?

Answer 4

Correct. You have the following sequence of numbers leading up:
\[\eqalign{
&f(n)=5+f(n-1);n\gt2 \\
&\\
&f(1)=2 \\
&f(2)=3 \\
&f(3)=8 \\
&f(4)=13 \\
&f(5)=18 \\
}\]

Answer 5

Okay. Thank you!

Answer 6

No problem!