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

Algebra.Com
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(20056)   (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
RELATED QUESTIONS

What is the next number in the sequence? 1 , 4 , 9 , 61 , 52 , 63 , 94 , 46 , 18 , 1 , (answered by Edwin McCravy)
what is the next term in the sequence below? 1, 8, 27,... (answered by Alan3354)
What is the next term in the sequence below? 1, 3, 5, 8, 11, 15, 19, 24, . .... (answered by jim_thompson5910)
For this problem in Newtons law of cooling, what does the e mean? Why do we use ln and... (answered by stanbon,MathLover1)
What is the next term in the sequence 44/36, 251/216, 1393/1296, 8051/7776 And why? (answered by ikleyn)
I need help with the following problem: In the following sequence, what could be the... (answered by ankor@dixie-net.com)
Harmonic sequence: 2,2/3,2/5,2/7 with solution What is the next term in the... (answered by Edwin McCravy)
-7,-7,-7/10,-7/80,-7/80,-7/800 What is the next term in this... (answered by ikleyn)
What is the next term in the geometric sequence 16, -4, 1,... (answered by vleith)