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

@LogicalApple I'm lost with this one!

Answer 2

Directly substitute n = 5 into the formula.

f(5) = f(1) + f(2) + f(4) .. Keep this in mind. We know f(1) = 2, and f(2) = 4 so

f(5) = 2 + 4 + f(4) = 6 + f(4). Now determine f(4) . . .

f(4) = f(1) + f(2) + f(3) = 6 + f(3)... so..

f(5) = 6 + (6 + f(3) ) = 12 + f(3) etc... can you take over ?

Answer 3

No :/

Answer 4

Here is the general rule: f(n) = f(1) + f(2) + f(n - 1)

Let n = 3

f(3) = f(1) + f(2) + f(3 - 1) = f(1) + f(2) + f(2)

Answer 5

I'm sorry I just do not get it.

Answer 6

Recursion is a little difficult to get at first. Let's start over.

We know the general rule of the function for any n. I.e., f(n) = f(1) + f(2) + f(n - 1). So far so good ?

Answer 7

Yes

Answer 8

We also know the value of f(1) and f(2). f(1) = 2, f(2) = 4. So we can rewrite f(n) as..

f(n) = 2 + 4 + f(n -1) = 6 + f(n - 1).

Answer 9

See if you can now determine f(3) knowing that f(n) = 6 + f(n - 1)

Answer 10

f(3) = 6 + f(0)?

Answer 11

f(n) = 6 + f(n-1)

Let n = 3

f(3) = 6 + f(3 - 1) = 6 + f(2)

Answer 12

Oh okay, you're right... sorry ^_^

Answer 13

f(4) = 6+f(4-1)
f(4) = 6+f(3)?

Answer 14

Yep . . but first what is f(3)? We have enough information to determine f(3).

f(3) = 6 + f(2)

Remember, f(2) is defined already.

Answer 15

f(3) = 6+4
f(3) = 10

Answer 16

Perfect! Now that you know f(3), what is your value of f(4) ?

Answer 17

f(4) = 16

Answer 18

And finally, f(5) ?

Answer 19

f(5) = 6+16
f(5) = 22

Answer 20

Nice.

Answer 21

Thank you so much!!!

Answer 22

so what is the answer?