Question

Write a recursive definition for the sequence:

5, 22, 36, 55

I'm completely unclear on how to do this. I would love some help. @mathmale @BTaylor

Answer 1

*39, 56

Answer 2

First describe the relation between the numbers using words

Answer 3

Do you see any pattern?

Answer 4

The difference of 17?

Answer 5

Yep

Answer 6

It goes up by 17 each time is what I meant.

Answer 7

How would you find the next term?

Answer 8

Add 17 to equal 73

Answer 9

Full sentence please

Answer 10

The next term in the sequence can be found by adding 17 to the pervious term.

Answer 11

Exactly, now write it in Mathematical notation

Answer 12

This is already recursive

Answer 13

How do I do that?

Answer 14

Either you use \(a_n\) for the previous term and \(a_{n+1}\) for the next,
or you use \(a_{n-1}\) for the previous term and \(a_n\) for the next.

Answer 15

\[a _{n} = a_{n} + 17\] ?

Answer 16

No

Answer 17

Oh

Answer 18

\(\Large a_{n+1}=a_n+17\)

Answer 19

Or \(\Large a_n=a_{n-1}+17\)

Answer 20

Why does there have to be the +1 or -1?

Answer 21

Because \(a_n\) is the n-th term of the sequence and \(a_{n+1}\) is the n+1.th term

Answer 22

For example \(a_1\) is the first term which is 5

Answer 23

Oh, okay. Now is that the end result or for my answer do I need to include the word version and the mathematical notation since it is a definition?

Answer 24

No you don't need to the word version

Answer 25

However you need to have one more detail

Answer 26

Only knowing that the next term is the previous term add 17 is not enough

Answer 27

Okay, thank you very much. Can you also help me with making an explicit formula for the sequence 4, 1.5, -1, -3.5 ?

Answer 28

But you know the answer for the first question now?

Answer 29

I know it goes up by -2.5 so Is it the same as the first problem?

Answer 30

Kind of, but now you're not required to find a recursive formula

Answer 31

No no, different problem. I need help with the explicit formula for the sequence 4, 1.5, -1, -3.5

Answer 32

I know

Answer 33

What's the common difference?

Answer 34

Sorry, I'm confused ha

second problem: The next term in the sequence can be found by adding -2.5 to the pervious term.

Answer 35

Therefore the common difference is?

Answer 36

2.5 ?

Answer 37

Good :)

Answer 38

Now find the difference between the common difference and the first term

Answer 39

so 4 - 2.5 = 1.5 ?

Answer 40

Wait... sorry the common difference is not 2.5 (hint: you're close :D)

Answer 41

But 4 - 1.5 = 2.5 and so do the other?

Answer 42

Yep, but you subtract the previous term from the next not vice versa

Answer 43

Do you mean -1 - 2.5 ?

Answer 44

I'm sorry can you show me an example with different numbers or something?

Answer 45

Okay I'll stop you from wondering, the common difference is -2.5 instead of 2.5

Answer 46

Because you add -2.5 to get the next term

Answer 47

Thats what I said though ha

Answer 48

Sorry lol

Answer 49

Oh sorry I see what I did ha I see it now

Answer 50

No no I wrote it twice but one as -2.5 and one as 2.5 so my apologizes :P

What do I do next?

Answer 51

You find the difference between the common differnece and the first term

Answer 52

Sorry for the typo

Answer 53

It's okay, what do I do after that?

Answer 54

Found it?

Answer 55

6.5 ?

Answer 56

Yep

Answer 57

Therefore \(\Large a_n=-2.5n+6.5\)

Answer 58

Thank you!

Answer 59

No problem

Answer 60

I have to go to dinner now but I still have some questions, will you be on later?? @kc_kennylau

Answer 61

Depends on the time...

Answer 62

Okay, well hopefully I'll be able to catch you. Thank you again!

Answer 63

No problem :)