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The task starts cancelled with the fair straightforward problem of trying to discovery the nth term formula for the triangular numbers.
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How are the triangular numbers used in stellar numbers?
A more interesting method makes use of the triangular numbers. We can first note a recurrence relationship in the stellar numbers – each subsequent pattern contains all the previous patterns inside. In fact we can state the relationship as: The outside star edge of S 2 can be thought of as 6 copies of the 2nd triangular number
How to find the formula for a stellar number?
We can then generalise to find stellar number formulae for different numbers of vertices. For example the 5-stellar numbers pictured above have the formula 5n 2 – 5n + 1. In fact the p-stellar numbers will have the formula pn 2 – pn + 1.
How to find the nth term for 6 stellar numbers?
Once this is done, we are asked to find the nth term for the 6-stellar numbers (with 6 vertices) below: Once again we can use the method for quadratic sequences. The second difference is 12, giving us an 2 + bn + c with a = 12/2 = 6.
Last Update: Oct 2021
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20.10.2021 07:36
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