How do you find the seventeenth term in the arithmetic sequence for which a=4.5 and d=0.2?

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Answer 1 · 2016-02-01T17:47:11

seventeenth term#=7.7#

Recall the general term in an arithmetic sequence is written as:

#t_n=a+(n-1)d#

where:
#t_n=#term number
#a=#first term
#n=#number of terms
#d=#common difference

To solve for the seventeenth term, substitute your known values into the equation:

#t_n=a+(n-1)d#

#t_17=4.5+(17-1)(0.2)#

#t_17=4.5+(16)(0.2)#

#t_17=4.5+3.2#

#color(green)(t_17=7.7)#

Note that the seventeenth term is also #t_17=a+16d#. If you used this equation, it would produce the same answer:

#t_17=a+16d#

#t_17=4.5+16(0.2)#

#t_17=4.5+3.2#

#color(green)(t_17=7.7)#

#:.#, the seventeenth term is #7.7#.