SOLUTION: What is the next term in the sequence below? 1,7,25,61,121,____ Why does my answer make sense?

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Question 734425: What is the next term in the sequence below?
1,7,25,61,121,____
Why does my answer make sense?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1,7,25,61,121,____
Hmm.  That's close to the increasing sequence of cubes,
which is this sequence:

1,8,27,64,125,...

Let's form a sequence of differences from the sequence of cubes:

1-0,8-1,27-2,64-3,125-4,

Aha, so

1 = 1³ - 0
7 = 2³ - 1
25 = 3³ - 2
61 = 4³ - 3
121 = 5³ - 4

So the next one is 6³-5 = 211

The nth term is n³-(n-1) or 

an = n³-n+1

Edwin