The 3rd term of an arithmetíc sequence is -I and the 7th term is -13. What is the explicit formula for this sequence? What is #a_22#?

1 Answer
Jim G.
Nov 29, 2017

#a_n=8-3n#

Explanation:

#"the nth term of an arithmetic sequence is"#

#•color(white)(x)a_n=a+(n-1)d#

#"where a is the first term and d the common difference"#

#"we require to find a and d"#

#a_3=a+2d=-1 to(1)#

#a_7=a+6d=-13 to(2)#

#"subtract "(1)" from "(2)#

#rArr4d=-12rArrd=-3#

#"substitute this value in equation "(1)#

#a-6=-1rArra=5#

#rArra_n=5-3(n-1)=8-3nlarrcolor(blue)"explicit formula"#

#rArra_(22)=8-66=-58#

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