Math Is Fun Forum

shirou

Guest

nth term

I need an explanation on how this formula works, to find the nth term.
I have been using:
a+(n-1)d+0.5[(n-1)(n-2)c]
d = the first difference
C = The difference increase.
a = the first term.

So, first of all, is this formula correct?
And how would you work it out, step by step, with a pattern like:
2, 5, 10, 17, 26....

What would the equation for n be with that pattern?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: nth term

Yep, that formula looks correct to me. To use it, just work out the three variables it asks for and put them it.

Sequence:    2, 5, 10, 17, 26
Differences:  3, 5, 7, 9

So the first difference is 3, the differences increase by 2 and the first term is clearly 2.

So the nth term is 2 + (n-1)3 + 0.5(n-1)(n-2)2
= (n-1)(n-2) + 3(n-1) + 2
= n² - 3n + 2 + 3n - 3 + 2
= n² + 1

It's easily verified that that works.

---

Why did the vector cross the road?
It wanted to be normal.

Shirou

Guest

Re: nth term

Ah, that makes more sense now.
I went and looked back at it and realized I had plugged in the wrong number for a. Eheh..
Thank you for replying. : )