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

1 Answer
Jan 25, 2016

Answer:

#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#