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April 14th, 2015, 05:42 PM  #1 
Senior Member Joined: Jan 2015 From: USA Posts: 107 Thanks: 2  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? 
April 14th, 2015, 06:17 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,634 Thanks: 2620 Math Focus: Mainly analysis and algebra 
Its an arithmetic series, not an arithmetic sequence. Investigate $$b_n = a_n  a_{n1} = An^2 + Bn  A(n1)^2  B(n1)$$ This gives you the difference between consecutive partial sums of the series. You can then look at $b_n  b_{n1}$ to find the difference between successive terms of the sequence. Last edited by v8archie; April 14th, 2015 at 06:20 PM. 
April 14th, 2015, 06:50 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, matisolla! Where did this problem come from? It makes little sense. Quote:
This is NOT an arithmetic sequence. The common difference, , is not constant.  

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