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How do you write the nth term rule for the arithmetic sequence with #d=5/3# and #a_8=24#?

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1 Answer

Jul 22, 2016

#a_n = 1/3(32+5n)#

Explanation:

The #n^(th)# term of an arithmetic sequence in terms of the #m^(th)# term and the common difference #(d)# is given by:

#a_n = a_m + (n-m)d#
In this example; #m=8, d=5/3# and #a_8 = 24#

Replacing these values into the general formula above#->#
#a_n = a_8+(n-8)*5/3#

#a_n = 24+(n-8)*5/3#
#=1/3(72+5n-40)#

#=1/3(32+5n)#

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