A level maths arithmetic series proof

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pondering-soul
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Sorry for the rant, but I'm sooooo frustrated and confused. I just.... I dont get it!!!

In what world.... is the sum of those two series.... n-1. It just... I can't seem to get (n-1) no matter what I do! It seems as clear as day.... so simple... yet it never adds to n-1! Every time, I get n d . Can someone help me understand this?


thanks a lot for any help I really appreciate it
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DFranklin
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First term of the first series is a.
First term of the second series is a + (n-1)d.
Add them and you get 2a + (n-1)d.

Second term of the first series is a + d
Second term of the second series is a + (n-2)d.
Add them and you get 2a + (n-1)d.

Etc...
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pondering-soul
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(Original post by DFranklin)
First term of the first series is a.
First term of the second series is a + (n-1)d.
Add them and you get 2a + (n-1)d.

Second term of the first series is a + d
Second term of the second series is a + (n-2)d.
Add them and you get 2a + (n-1)d.

Etc...
thanks bro I needed that
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