It is also possible to just define it by cases, one for when sequence term is even and one where term is odd.HAF said:Hello, i have a sequence {1,2,13,62,313...} and I have to find out the rule for n-th number. I've found out that every next number is five times bigger but then is added or subtracted 3. For example 1x5 -3 = 2 and 2x5 +3 = 13 and so on. Can you please give me some advice how to create the general formula of this sequence?
Thank you
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.WWGD said:It is also possible to just define it by cases, one for when sequence term is even and one where term is odd.
Yes, I mean, my description may not be the best by reasonable standards, but it does describe the sequence fully.jbriggs444 said: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.