Respuesta :

caylus
Hello,

[tex] u_{1}=5\\ u_{2}=15=5*3\\ u_{3}=45=5*3^2\\ u_{4}=135=5*3^3\\ \boxed{u_{n}=5*3^{n-1}}\\\\ u_{6}=5*3^5=1215\\ [/tex]

The 6th term of this geometric sequence is 1215.

To understand more, check below explanation.

Geometric sequence:

The general term of geometric series is given as;

                 [tex]a_{n}=a*r^{n-1}[/tex]

Where a is first term and r is common ratio.

Given sequence is,

               5, 15, 45, 135

So that, [tex]a=5,r=15/5=3[/tex]

We have to find 6th term,

                 [tex]a_{6}=5*3^{6-1} \\\\a_{6}=5*3^{5} \\\\a_{6}=5*243=1215[/tex]

Therefore, the 6th term of this geometric sequence is 1215.

Learn more about the geometric sequence here:

https://brainly.com/question/24643676