How to give inductive definition to sequence?

Give inductive definition for the following:

1). 120, 60, 30, 15, 7.5, …
2). 4, 9, 19, 39, 79, …

What two things do you need to define a sequence inductively?

No idea. I can only define arithmetic sequences using a and d.

That's kind of like an inductive definition for a sequence, in that the first term, = a, and you're given that $a_1 = a$ and
$a_{n+1} = a_{n} + d$.

Does that help?

I don't think you can use that for the sequences I posted.

Then the question would be impossible to solve

The answers aren't going to look exactly like that but something similar.

What is the first term in sequence 1? And what is the relationship between two consecutive terms?

That's where the sequence starts and the relationship isn't stated.
There is no extra information, that's all that's given.

You are reading my questions in the wrong way

That is where the sequence starts, yes, so the first term must be there at the start.

The relationship isn't stated but you should be able to identify it.

I know the relationship, but now how would I turn it into an inductive definition? Also here's another sequence: 1, 3, 11, 43, 171, … relationship is a bit harder to find there but I still can't turn it into a I.Definition.

That's where the sequence starts and the relationship isn't stated.
There is no extra information, that's all that's given.

Sean isn't asking for extra information - you should be able to answer the questions by looking at the given values and *thinking*. Explicity: try to think what operation(s) you might use to get from 120 to 60, and from 60 to 30, and so on.

I know how to find the relationship but then how do I turn it into a inductive definition?

OK, explain what the relationship is.

x1/2 to get next term

So what is an algebraic relationship connecting a given term $u_n$ with the next term in the sequence, $u_{n+1}$

1/2Un?

Yes, $u_{n+1} = \frac{1}{2}u_n$

Then this, together with your first term $u_1 = 120$ is your inductive definition:

$u_1 = 120, u_{n+1} = \frac{1}{2}u_n$

Is this how it will always be written: Un+1 = Un + c or Un+1 = Un

Or can you have indices or brackets aswell?

e.g. Un+1 = (Un -3)^2 -3/4


If not then I just need to find out what I can times Un by then what I need to add or subtract after that to get the next term?

The relationship between successive terms could be anything, it could involve adding, multiplying or indices.

What it will actually involve in your exam depends on your specification. If it is for A Level I do not imagine the recurrence relationship (the relationship between two consecutive terms) will be too complicated.