Given that the first term of a geometric progression is 8 and the sum of the first three terms is 104, find the possible values of the common ratio. In each case, write down the corresponding first three terms of the series. ?

1 Answer
Jim G.
Jul 9, 2018

#8,24,72" and "8,-32,128#

Explanation:

#"using the n th term formula for a geometric progression"

#•color(white)(x)a_n=ar^(n-1)#

#"where a is the first term and r the common ratio"#

#"here "a=8#

#S_3=a+ar+ar^2=104#

#" or "8+8r+8r^2=104larrcolor(blue)"solve for r"#

#1+r+r^2=104/8=13#

#r^2+r-12=0larrcolor(blue)"in standard form"#

#(r+4)(r-3)=0#

#"hence "r=3" or "r=-4#

#r=3to8,8xx3,8xx9=8,24,72#

#r=-4to8,8xx-4,8xx(-4)^2=8,-32,128#

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