# Maths: Sequence

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#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?
0
16 years ago
#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.
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#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.
0
16 years ago
#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.
0
16 years ago
#5

Very good indeed.
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#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.
0
16 years ago
#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.
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16 years ago
#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.
0
16 years ago
#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
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16 years ago
#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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