Asked by Fred
                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.
            
        How can we do this without trial and error? Thanks to anyone who helps.
Answers
                    Answered by
            Anonymous
            
    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 : )
    
                    Answered by
            Ms Pi_3.14159265
            
    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 : )
    
                    Answered by
            Reiny
            
    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
    
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
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