what is the closed linear form for sequence a1=13 and an+1=an+4

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14-03-2017
Mathematics

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what is the closed linear form for sequence a1=13 and an+1=an+4

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LammettHash LammettHash · Answer 1 · 2017-03-14T20:21:52+01:00

LammettHash LammettHash

14-03-2017

[tex]a_{n+1}=a_n+4[/tex]
[tex]a_{n+1}=(a_{n-1}+4)+4=a_{n-1}+2\times4[/tex]
[tex]a_{n+1}=(a_{n-2}+4)+2\times4=a_{n-2}+3\times4[/tex]

and so on, until you're left with

[tex]a_{n+1}=a_1+4n=4n+13[/tex]

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