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.

Answer 1

I did it my way and it came out 10. Not sure if im doing it right tho

Answer 2

10 is correct for the third term. You still need to find the 4th and then the fifth term.

Answer 3

Ok then im doing something wrong. can you explain to me how to do the 4th one correctly and then i can do the 5th one?

Answer 4

Sure. The first thing I would do is to simplify the original equation because you have two constants in the nth term.

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

put n = 3
f(3) = 6 + f(2) = 6 + 4 = 10

put n = 4
f(4) = 6 + f(3) = 6 + 10 = 16

Answer 5

Ok so f(5) will go like this?

f(5) = 6 + f(4) and f(4) equaled 16 so f(5) = 6 + 16 = 22.
f(5) = 22?

Answer 6

Yes!

Answer 7

Just another one for practice.
For f(6)
f(6) = 6 + f(5) and f(5) was 22 so f(6) = 6 + 22 =28?

Answer 8

If you examine the f(n) formula you can quickly figure out how to easily get other terms.

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

It says the nth term is 6 added to the previous term.

So 6th term = 6 + 5th term = 6 + 22 = 28
7th term = 6 + 6th term = 34

Yes your sixth term is correct too. You got it!

Answer 9

Thanks!

Answer 10

you are welcome.