The two geometric means between 3 and 5184 are 36 and 432: Option D is correct.
Since we are to find 2 geometric means between 3 and 5184, the number of terms of the sequence will be 4.
The formula for finding the nth term of a geometric sequence is expressed as;
[tex]T_n = ar^{n-1}[/tex]
a is the first term = 2
r is the common ratio
n is the number of terms
The sequence of numbers will be 3, x, y and 5184
r³ = 5184/3
r³ = 1728
r = 12
Get the second term of the sequence
[tex]T_2 = 3(12)^{2-1}\\T_2=3\times 12\\T_2 = 36[/tex]
Get the third term of the sequence
[tex]T_3 = 3(12)^{3-1}\\T_3=3\times 144\\T_3 = 432[/tex]
Hence the two geometric means between 3 and 5184 is 36 and 432
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