The 10th term of the geometric sequence is given as follows:
[tex]a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}[/tex]
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
Using the mth term as the reference, we have that:
[tex]a_n = a_mq^{n-m}[/tex]
Hence:
[tex]a_5 = a_3q^2[/tex]
[tex]q = \sqrt{\frac{a_5}{a_3}}[/tex]
And then the 10th term is given as follows:
[tex]a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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