What is the recursive formula for the sequence #4, 12, 20,...# ?

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Answer 1 · 2017-02-22T23:33:02

#{ (a_1 = 4), (a_(n+1) = a_n + 8 " for " n >= 1) :}#

As far as it goes, this is an arithmetic sequence with common difference #8#, since:

#12 - 4 = 8#

#20 - 12 = 8#

So we can describe it recursively by:

#{ (a_1 = 4), (a_(n+1) = a_n + 8 " for " n >= 1) :}#

Alternatively, a direct formula is given by:

#a_n = 4 + 8(n-1)#

or if you prefer:

#a_n = 8n - 4#