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# HELP! Sequences! Watch

1. Right

Mid-homework and I'm stuck on how to "prove that the sum of the first n terms of the series is

1/2n[2a+(n-1)d]

I've searches on other threads and there is one with the same problem, however I don't really understand it to be honest.

ALL HELP WELCOME!!! Thanks!
2. (Original post by ModMod)
Right

Mid-homework and I'm stuck on how to "prove that the sum of the first n terms of the series is

1/2n[2a+(n-1)d]

I've searches on other threads and there is one with the same problem, however I don't really understand it to be honest.

ALL HELP WELCOME!!! Thanks!
...Doesn't really mean anything unless you tell us what the series is....
3. All it says is "first term a and common difference d

I should've probably mentioned that in the question !
4. Write out the first n terms of the series as a, a+d, a+2d, ... , a+(n-1)d

Can you see a way to sum them nicely? The formula given is a clue
5. (Original post by ModMod)
Right

Mid-homework and I'm stuck on how to "prove that the sum of the first n terms of the series is

1/2n[2a+(n-1)d]

I've searches on other threads and there is one with the same problem, however I don't really understand it to be honest.

ALL HELP WELCOME!!! Thanks!
Well you haven't explained your existing knowledge so I am assuming this is AS mathematics.

Write down the arithmetic series in full:

a + (a + d) + (a + 2d) + (a + 3d) + .... I will let you figure out the last term

Now write the same series backwards underneath

Add the two series together (the terms will pair off)

This will give you twice the sum ...
6. Great! Thanks!

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