How do you find the 12th term of the arithmetic sequence 20, 14, 8, 2, -4, ...?

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Answer 1 · 2015-12-20T08:15:33

#12^(th)# term#=-46#

A term of an arithmetic sequence can be calculated with the formula:

#t_"n"=a+(n-1)d#

where:
#t_"n"=#any term in the arithmetic sequence
#a=# first term
#n=# term number/number of terms
#d=# common difference

To find the #12^(th)# term of the sequence, we first need to find #d#, the common difference. We can do this by subtracting #t_"1"# from #t_"2"#:

#t_"2"-t_"1"#
#=14-20#
#=-6#

Now that you have the common difference, substitute all your known values into the formula to solve for #t_"12"#:

#t_"n"=a+(n-1)d#
#t_"12"=20+(12-1)(-6)#
#t_"12"=20+(11)(-6)#
#t_"12"=20-66#
#t_"12"=-46#

#:.#, the #12^(th)# term is #-46#.