Question

Find f(1), f(2), and f(3) if f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . .

• f(n+1) = f(n) + 2

So, would it be f(n) = f(n+1) + 2? Or would I just keep it like the original and plug in 1, 2, 3. Thanks for any helpful replies.

Answer 1

Ok thank for the responses, but there seems to be a contradiction between the two. Wouldn't f(1) = 1 + 2, which equals 3?

Answer 2

Almost!
What you have done was for
f(n+1)=f(n)+3, and f(1)=3.
so f(2)=f(1)+3=3+3=6
f(3)=f(2)+3=6+3=9.

If you are solving f(n+1)=3f(n) with f(1)=3, then
f(2)=3*f(1)=3*3=9
f(3)=3*f(2)=3*9=27
f(4)=3*f(3)=3*27=81,
...
effectively a geometric sequence instead.

Answer 3

f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . .

Find f(1), f(2), f(3)

Answer 4

As Damon mentioned, it is an arithmetical sequence (or in general, any sequence).
So the zeroth term is denoted f(0), the 1st term f(1), etc.
So for
1,3,5,7,9,...
f(0)=1
f(1)=3
f(2)=5
...
the relation between them is therefore
f(n+1)=f(n)+2

This is called a recurrence relation, and you can only evaluate a certain term if the previous terms are know.

For the Fibonacci sequence, it would be
f(n)=f(n-1)+f(n-2)
f(0)=0
f(1)=1

so
f(2)=f(1)+f(0)=1+0=1
f(3)=f(2)+f(1)=1+1=2
f(4)=f(3)+f(2)=2+1=3
f(5)=f(4)+f(3)=3+2=5
....
to give the Fibonacci sequence
1,1,2,3,5,8,13,21,34....

Answer 5

The f(n+1) is throwing me off what does that mean?

Answer 6

just add 2 each time
f(0) = 1
f(1) = 3
f(2) = 5
f(3) = 7 etc
That is an arithmetic sequence
f(n) = 1 + 2n

Answer 7

Oops. . .Sorry disregard previous post. . .

Answer 8

Is this the previous problem where f(n)=f(n-1)+3, or is this a new problem?

I don't see the recursive definition of f(n).

Answer 9

OK example: f(n+1) = 3f(n)

f(1) = 3
f(2) = 6
f(3) = 9

Right?

Answer 10

As in algebra, put your known values on the right hand side, and the quantity to be evaluated on the left. Follow the definition of the function.

So if f(0)=1, then n=0, therefore
f(1)=f(0)+2
...

Answer 11

Yes, they both follow the same recursive definition. I was just trying the second part on my own to see if I understand. Sorry about the misunderstanding. . .

Answer 12

OK example: f(n+1) = 3f(n)

f(1) = 3
f(2) = 6
f(3) = 9

Right?