Answer:
f(n) = 0.1867/(6.067)^(n-1)
Step-by-step explanation:
The general form for the nth term is a1 r^(n-1) where a1 = first term and r = common ratio.
So we have, from the info given:
a1 r^2 - a1 = 48
a1 r^2 * a1 = 9
From the second equation:
a1 r^2 = 9 / a1
Substitute for this in the first equation:
9 / a1 - a1 = 48
9 - a1^2 = 48a1
a1^2 + 48a1 - 9 = 0
a1 = 0.1867, -48.18
so r^2 = 9 / (a1)^2
r = 16.07 , 0.003878.
a1 = 0.1867 when r = 16.067
a1 = -48.18 when r = 0.003878.
Only the first 2 values fit the original equations.
