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) = ______

Numerical Answers Expected!

Answer for Blank 1:

Answer 1

@mathstudent55

Answer 2

Plug in the values to your recurrence relation for f(1) and f(2). It will make it much easier I think!

Answer 3

Here is an explanation of what this means:
f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(1) is the first term of the sequence. We are given f(1) = 2
f(2) is the 2nd term of the sequence, and we are told f(2) = 3
There are no calculations needed to find the first two terms. they are given.

Answer 4

To calculate any term past the second term, when n > 2, then you use the given formula.
f(n) = f(1) + f(2) + f(n - 1)
That means that any term of the sequence (past the second term) is the sum of the first term, the second term, and the previous term.

Answer 5

Using the formula, let's see what we get for the 3rd term.
The third term has n = 3.
We need to find
f(n) = f(1) + f(2) + f(n - 1) for n = 3
Let's see which terms we need to add.
We replace n with 3 in the formula:
f(3) = f(1) + f(2) + f(3 - 1)
f(3) = f(1) + f(2) + f(2)
f(3) = 2 + 3 + 3 = 8
That means the third term is 8.
Now you need to do the same calculation for n = 4 and then n = 5.

Answer 6

oh okay

Answer 7

how would I do the rest i'm not too sure how to set them up

Answer 8

Would it be 13 for the 5th term?

Answer 9

@mathstudent55

Answer 10

Let's see. I need the 4th term first.
f(4) = f(1) + f(2) + f(4 - 1)
f(4) = f(1) + f(2) + f(3) = 2 + 3 + 8 = 13

f(5) = f(1) + f(2) + f(5 - 1)
f(5) = f(1) + f(2) + f(4) = 2 + 3 + 13 = 18

Answer 11

oh okay so I said the 4th term okay. Well thank you so much!

Answer 12

Notice that each term is the previous term plus the first two terms.
The first two terms are always 2 and 3, so you are always adding 5 to the previous term.

Answer 13

Alright

Answer 14

2
3
2 + 3 + 3 = 8
5 + 8 = 13
5 + 13 = 18
5 + 18 = 23
5 + 23 = 28
etc.

Answer 15

You're welcome.

Answer 16

oh okay I got it now. Thank you so much for explaining it to me