I am trying to find a formula to express the nth term, the pattern is as follows:
n = 4, 5, 6, 7
its corresponding values are as follows:
6, 10, 15, 21
I know this is not worded very well, if anyone can help it would be most appreciated
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$$ \begin{align} x + 3 & = 6 \ 6+4 &=10 \ 10+5 &= 15 \ 15+6 &= 21 \ \end{align} $$ – Bennett Gardiner May 07 '14 at 03:36
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1Note the seventh term is the sixth term plus six. – grantfgates May 07 '14 at 03:37
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http://en.wikipedia.org/wiki/Triangular_number – Bennett Gardiner May 07 '14 at 03:39
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The pattern is as follows: $$a_{n-3}=\dfrac{n(n-1)}{2},a_0=6$$ Or alternately, $$a_{n-3}=a_{n-4}+(n-3),a_4=6$$
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Thank you, the n(n-1)/2 is what I was looking for. Is there a name for a topic I can look up in order to help figure these out? I would never be able to see it on my own – user3371750 May 07 '14 at 03:40
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@user3371750 If this answer is what you needed click the green check mark to select this answer as the correct one, and/or vote it up if you like it. – May 07 '14 at 03:42