How do you write a rule for the nth term of the arithmetic sequence #a_8=19/5, a_12=27/5#?

1 Answer
Jim G.
Mar 8, 2017

#a_n=2/5n+3/5#

Explanation:

For the standard #color(blue)"arithmetic sequence"#

#a,a+d,a+2d,a+3d,........,#

The nth term is #• a_n=a+(n-1)d#

where a is the first term and d, the common difference.

For the sequence in question we have to find a and d

#rArra_8=a+7d=19/5to(color(red)(1))#

#rArra_(12)=a+11d=27/5to(color(red)(2))#

#(color(red)(2))-(color(red)(1))# gives d

#rArr4d=8/5rArrd=2/5#

Substitute this value into #(color(red)(1))#

#rArra+14/5=19/5rArra=1#

We can now obtain the nth term rule.

#rArra_n=1+2/5(n-1)#

#rArra_n=2/5n+3/5larrcolor(red)" nth term rule"#

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