write explicit formula for sequence 3, 6, 17, 35, 62, 97

[cshw20]

Q: Write an explicit formula for the following sequence: 3, 6, 17, 35, 62, 97

I understand that the difference between the sequence is 3, 11, 19, 27, 35, 43 and that the difference between each of these numbers is 8.

I have been able to come up with explicit formulas for more obvious sequences but cannot determine this one.

Thank you for your help.

 

[royhaas]

Re: Sequences - Explicit formula

When the second difference is a constant, it means that a parabola will pass through any three points.

 

[Denis]

Re: Sequences - Explicit formula

There's 2 formulas for these: what's the sum of first n terms, and what's the nth term?

Both easy enough to get: www.trottermath.net/algebra/vantris.html

You'll see that sum of first n terms is: 3n + 3n(n - 1) / 2 + 8n(n - 1)(n - 2) / 6
I'll let you simplify it.

 

[cshw20]

Re: Sequences - Explicit formula

Thank you for your help and for the link Denis. I now understand.