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| − | The recurrence relation is an equation relating <math>a_n</math> to previous values of <math>a_n</math> i.e. <math> | + | The recurrence relation is an equation relating <math>a_n</math> to previous values of <math>a_n</math> i.e. <math>a_{n-1}</math>. For example, a recurrence relation would be <math>a_n</math> = <math>a_{n-1}</math> + 2. |
In part b), you are asked for an explicit formula. This is an equation from which we can compute <math>a_n</math> directly. i.e. <math>a_n</math> = 27n. | In part b), you are asked for an explicit formula. This is an equation from which we can compute <math>a_n</math> directly. i.e. <math>a_n</math> = 27n. | ||
Revision as of 11:13, 19 October 2008
I'm a bit confused by the phrasing of this problem. Is the recurrence relation just the $ a_n $ statement without the initial conditions?
I am confused as well, anyone have any diection? -ERaymond 10/16/08 10:20am
The recurrence relation is an equation relating $ a_n $ to previous values of $ a_n $ i.e. $ a_{n-1} $. For example, a recurrence relation would be $ a_n $ = $ a_{n-1} $ + 2.
In part b), you are asked for an explicit formula. This is an equation from which we can compute $ a_n $ directly. i.e. $ a_n $ = 27n. However, in general, I dont think it is always possible to obtain an explicit forumla.
Note: you will need some initial conditions to derive the explicit formula.
I hope this helps,
Tom --Tsnowdon 15:05, 19 October 2008 (UTC)
