Question

A recursive function is shown below: f(1) = 5 and f(n) = f(n - 1) - 6; n > 1 Which of the following lists the terms in the sequence defined by this recursive function?
A .5, 1, 7, 13, 19, ...
B. 5, -1, -7, -13, -19, ...
C. 5, 11, 17, 23, 29, ...
D. 5, -11, -17, -23, -29, ...

Answer 1

Please help! :)

Answer 2

Can you find second term? \(f(2) = f(2-1) - 6\ = \cdots~?\)

Answer 3

Im not so good at this, do you think you could explain to me how so i could try?

Answer 4

We know that first term is \(f(1) = 5\), right?

And you were given that \(f(n) = f(n-1)-6\)

So for next term, you have \(f(2) = f(2-1)-6 \\~~~~~~~= f(1)-6 \\~~~~~~~= 5 - 6 \\~~~~~~~=~ ?\)

Answer 5

Does that help?

Answer 6

that makes sense but, i still do not know how to find the answer @geerky42

Answer 7

Can you be more specific on what don't you understand?

Answer 8

what im getting from what you wrote is the simple answer -1. ? what would we do to find the actual answer i guess im confused on

Answer 9

like i said im really bad at this so sorry!

Answer 10

You were asked to find sequence of terms, you just need to find \(f(1),~f(2),~f(3),~f(4),~\ldots \)

we already knew what \(f(1)\) is. Now we need to find next term: \(f(2)\).

So since \(f(\color{red}{n}) = f(\color{red}{n} - 1) - 6\), you have \(f(\color{red}{2}) = f(\color{red}{2}-1)-6\)

Obviously, \(2-1\) is \(1\), right?

So \(f(\color{red}{2}) = f(\color{red}{2}-1)-6\\~~~~~~~=f(1)-6\)

We know that \(f(1)=5\), so we can replace \(f(1)\) with \(5\)

So \(\cdots= 5 - 6\\~~~~~=-1\)

Now we know what second term \(f(2)\) is; it's -1.

So far, we know first two terms.

Answer 11

Omg thats so simple thank you so much!!

Answer 12

At first i didnt realize we were finding them for each "f"

Answer 13

Ok, welcome :)