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Thank you

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- #1

- 58

- 6

Thank you

- #2

DrClaude

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- #3

mfb

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- #4

WWGD

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It is also possible to just define it by cases, one for when sequence term is even and one where term is odd.

Thank you

- #5

jbriggs444

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If the solution is of the form ##a(-1^n) + b(5^n)## then one should be able to find a characteristic equation for it -- a quadratic with roots of -1 and 5. That characteristic equation would then suggest a recurrence relation. Which immediately yields a recursive rule for the n'th number in terms of the n-1'st and n-2'nd.It is also possible to just define it by cases, one for when sequence term is even and one where term is odd.

Yup. Works out quite easily. [It's been almost 40 years since I learned how to go from a recurrence relation to a formula. This is the first time I've gone the other way -- from a formula to a recurrence relation]

- #6

WWGD

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Yes, I mean, my description may not be the best by reasonable standards, but it does describe the sequence fully.If the solution is of the form ##a(-1^n) + b(5^n)## then one should be able to find a characteristic equation for it -- a quadratic with roots of -1 and 5. That, characteristic equation would then suggest a recurrence relation. Which immediately yields a recursive rule for the n'th number in terms of the n-1'st and n-2'nd.

Yup. Works out quite easily.

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