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

1 Answer
Feb 22, 2017

Answer:

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

Explanation:

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#