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# Maths: Sequence watch

1. What is the nth term of the sequence:

1 4 10 20 35

I'm aware the differences follow the triangle number secuence, but what do I do now?
2. I don't know much about the maths of triangle numbers, but I'd have a guess that n is the power of something.

Hmm... Well it's now obvious triangle numbers are just the addition of numbers, like a factoral where instead of multiplying you just add numbers.

I'll wait and see what other people have got.
3. (Original post by mik1a)
I don't know much about the maths of triangle numbers, but I'd have a guess that n is the power of something.
The nth term of the triangle number sequence is n(n+1)/2.
4. (Original post by ZJuwelH)
What is the nth term of the sequence:

1 4 10 20 35

I'm aware the differences follow the triangle number secuence, but what do I do now?
Those are tetrahedral numbers. The nth term is n(n+1)(n+2)/6.

Very good indeed.
6. (Original post by Squishy)
Those are tetrahedral numbers. The nth term is n(n+1)(n+2)/6.
Oh I see, like pyramid numbers.
7. (Original post by ZJuwelH)
Oh I see, like pyramid numbers.
Because the differences are the triange numbers, the nth term is the sum of the triangle numbers up to n. That is,

SUM{r=1 -> n} r(r+1)/2

You can use the fact that

SUM{r=1 -> n} r = n(n+1)/2
SUM{r=1 -> n} r^2 = n(n+1)(2n+1)/6

to work out the formula that Squishy quoted.
8. (Original post by samdavyson)

Very good indeed.
Thanks (if you were referring to me).

(Original post by ZJuwelH)
Oh I see, like pyramid numbers.
Yup, a tetrahedral number is a type of pyramidal number.
9. (Original post by mikesgt2)
Because the differences are the triange numbers, the nth term is the sum of the triangle numbers up to n. That is,

SUM{r=1 -> n} r(r+1)/2

You can use the fact that

SUM{r=1 -> n} r = n(n+1)/2
SUM{r=1 -> n} r^2 = n(n+1)(2n+1)/6

to work out the formula that Squishy quoted.

hello can u help me with maths its all about number grid i need the introduction if u can help me with plz
10. (Original post by ZJuwelH)
What is the nth term of the sequence:

1 4 10 20 35

I'm aware the differences follow the triangle number secuence, but what do I do now?
As Wittgenstein once said the next number (and therefore the nth term) can be anything you want it to be you just need a formula linking the numbers eg what is the next term in the following series: 1 2 3 4 5 6 7 8 9 ... Well it is 11, the nth term is [11n/10] where [x] is the integer part of x. Or it could be 0 where the the nth term is n (mod 10). Or it could be 10 - Ill let you work out the nth term for that series...

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