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# Nth Term - 2nd Diff! Watch

1. Q: Find the Nth term: 3 9 18 30 45

What I've done: 1st diff = 6 9 12 15....

2nd diff = 2

so the nth term involves n^2

dunno what to do next? what is an expression for the nth term?

cheeeers xxxxxxxxxxxx
2. n^2 = 1 4 9 16 25

is that relevant?
3. That sequence is just 3x the triangle numbers
Spoiler:
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4. the 2nd difference is 3 not 2
5. (Original post by Potassium^2)
That sequence is just 3x the triangle numbers
Spoiler:
Show
nice one!
6. If you get one of these where you don't spot a nice pattern (like it being a multiple of the triangle numbers), say you notice that the second difference is constant. Then you can let the nth term be equal to , and then you can substitute in three values of to find out what are. It's a bit of a pain to do though, so spotting a pattern is usually a good idea!
7. (Original post by nuodai)
If you get one of these where you don't spot a nice pattern (like it being a multiple of the triangle numbers), say you notice that the second difference is constant. Then you can let the nth term be equal to , and then you can substitute in three values of to find out what are. It's a bit of a pain to do though, so spotting a pattern is usually a good idea!
It's also worth knowing that,

if it's a quadratic sequence then the coefficicent of n^2 = second difference / 2!

and

if it's a cubic sequence then the coefficicent of n^3 = third difference / 3!

and so on.

You can also just write down the answer.

e.g. 3, 9, 18, 30, 45

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Updated: December 15, 2010
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