Help with the finite difference method

[maiden heart]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[hasty patrol]

Can someone help me with these questions pls

I don’t really understand the finite difference method

[calm crystal]

What I understand as finite difference method applies to differential equations, not discrete mathematics.
Would you mind clarifying what you meant?

[hasty patrol]

The textbook that I’m using just tells that there are general formulas that you could use, but it does not explain where that formulas came from

[calm crystal]

Would you mind providing us with the title and author?

Ah I see

[hasty patrol]

^^^

[calm crystal]

The method is naturally derived to find the general formula for sequences assuming the formula is a polynomial

e.g. each arithmetic sequence has a common difference, correspondingly each of them has a one-variable polynomial of degree 1 as their general formula

Similarly, every quadratic sequence has its common difference form an arithmetic sequence

So on so forth

So for a sequence with its general formula being a one-variable polynomial of degree n,
by checking the differences between its consecutive terms, and then the differences between the sequence of such differences, so on so forth for n times,
we will get a constant sequence like what we get for an arithmetic sequence

This is analogous to single-variable differentiation, in the continuous case

[hasty patrol]

Oh idk differentiation

But can you derive the general formula algebraically

Or can you give an example

@calm crystal

[calm crystal]

In my opinion, the example given in your book illustrates well enough to not necessitate me thinking up another

[calm crystal]

Upon a second look it even is the general case for quadratic sequences

[hasty patrol]

But how do u know that the general formula for the quadratic sequence un=an^+bn+c.

Like how did they derive

It’s like the standard form of a quadratic function

@calm crystal

[calm crystal]

They calculated the differences between consecutive terms
The differences then form another sequence, and then they found the difference between consecutive terms of that sequence too

[hasty patrol]

Can u give me an example pls

[calm crystal]

10, 5, 2, 1, 2, 5, 10, 17

[hasty patrol]

Oh as their second difference is a constant they r a quadratic sequence

[hasty patrol]

@calm crystal

[calm crystal]

You don't have to tag me everytime, I check followed posts now and then at my own pace, and have the server muted (so there is no audio notification)

So what's up?

[hasty patrol]

I kinda now get it

So TYSM @calm crystal

[fair finch]

@hasty patrol has given 1 rep to @calm crystal

[hasty patrol]

+close