Nth Term - 2nd Diff!

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

Reply 1

jim666666

OP

n^2 = 1 4 9 16 25

is that relevant?

Reply 2

Potassium^2

That sequence is just 3x the triangle numbers

Spoiler

Reply 3

whyisthatcrazy

the 2nd difference is 3 not 2

Reply 4

jim666666

OP

Original post by Potassium^2

That sequence is just 3x the triangle numbers

Spoiler

nice one!

Reply 5

nuodai

17

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

an^2+bn+c

, and then you can substitute in three values of

n

to find out what

a,b,c

are. It's a bit of a pain to do though, so spotting a pattern is usually a good idea!

Reply 6

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

5

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

an^2+bn+c

, and then you can substitute in three values of

n

to find out what

a,b,c

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

3\frac{(n-2)(n-3)}{(1-2)(1-3)}+9\frac{(n-1)(n-3)}{(2-1)(2-3)}+18\frac{(n-1)(n-2)}{(3-1)(3-2)}

Nth Term - 2nd Diff!

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