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April 14th, 2015, 05:42 PM   #1
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Demonstrate that An^2 + Bn is an arithmetic sequence

The problem is as the title states: Demonstrate that An^2 + Bn is an arithmetic sequence.

I don`t know how to solve this. Any ideas?
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April 14th, 2015, 06:17 PM   #2
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Its an arithmetic series, not an arithmetic sequence.

Investigate $$b_n = a_n - a_{n-1} = An^2 + Bn - A(n-1)^2 - B(n-1)$$
This gives you the difference between consecutive partial sums of the series.
You can then look at $b_n - b_{n-1}$ to find the difference between successive terms of the sequence.
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Last edited by v8archie; April 14th, 2015 at 06:20 PM.
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April 14th, 2015, 06:50 PM   #3
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Hello, matisolla!

Where did this problem come from?
It makes little sense.


Quote:
Demonstrate that is an arithmetic sequence.

I don't know how to solve this.
Any ideas?

This is NOT an arithmetic sequence.



The common difference, , is not constant.

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