Solve 6th Grade Sequence: 1,5,13,25,41,61

[debrawallenger]

Help, anyone. I am very new to this forum and am really here trying to help my son with his wicked 6th grade homework. His teacher is in my opinion, assigning problems that are way too difficult. I was hoping someone here could maybe help. The problem is as follows: The students are given the sequence 1,5,13,25,41,61 and have to come up with an equation to solve the sequence. Any ideas? This should be easy for you all. But for me, who was good at math at one time, this is beyond what I can come up with. Any help would be appreciated!

 

[Math Is Hard]

Hint: what's the difference between 5 and 1? 13 and 5? 25 and 13? 41 and 25? 61 and 41?
see the pattern?

oh, and Hi! Welcome to PF!

 

[Chronos]

Hmm, I see a pattern too. Counting up from zero 1, 4, 8, 12, 16, 20...

 

[debrawallenger]

I see the pattern as well, they are all separated by multiples of four, but it's coming up with the equation that is the problem. Any more hints? Maybe it will job something in my distance math past!

 

[arildno]

Sorry about that, I bungled up a bit..

 

[debrawallenger]

My mistake everyone,

I am going to post in the homework section. Thanks all. I also stated the problem incorrectly.

debra

 

[arildno]

From what I can see, the terms fulfill:
a_{n}=n^{2}+(n-1)^{2}