Question

For the geometric sequence t: {3, m, n, 192, . . .}, find the values for m and n.(Answer is m=12, n=48)

How can we do this without trial and error? Thanks to anyone who helps.

Answer 1

You have the first and the fourth term of the sequence. If you make equations for the first and fourth term you can use them to solve for r, and then sub it back into the original to find the second and third terms : )

Answer 2

You have the first and the fourth term of the sequence. If you make equations for the first and fourth term you can use them to solve for r, and then sub it back into the original to find the second and third terms : )

Answer 3

like this:

m/3 = n/m
m^2 =3n ---> m^4 = 9n^2

n/m = 192/n
n^2 = 192m

using m^4 = 9n^2
m^4 = 9(192m)
m^4 - 1728m = 0
m(m^3 - 1728) = 0
m = 0 , which it can't, since we would be dividing by 0
or
m^3 = 1728 , m = 12
in n^2 = 192m
n^2 = 192(12) = 2304
n = 48