How do you find r and a1 for the geometric sequence: a3 = 5, a8 = 1/625?

1 Answer
Alan P.
Jan 25, 2016

r=1/5
a_1=125

Explanation:

For a geometric series:
color(white)("XXX")a_m=a_n*r^(n-m)

We will use this general formula in two forms
color(white)("XXX")a_8=a_3*r^5
and
color(white)("XXX")a_1=a_3*r^(-2)

We are told a_8 = 1/625 and a_3=5
Therefore
color(white)("XXX")1/625 = 5*r^5

color(white)("XXX")r^5=1/(5*625) = 1/(5*5*4) = 1/(5^5)

color(white)("XXX")r=1/5

and since a_1=a_3*r^(-2)
color(white)("XXX")a_1= 5*(1/5)^(-2) = 5*5^2=125

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