Verified Answer :

caylus

Hello,

\(u_{1}=5\\ u_{2}=15=5*3\\ u_{3}=45=5*3^2\\ u_{4}=135=5*3^3\\ \boxed{u_{n}=5*3^{n-1}}\\\\ u_{6}=5*3^5=1215\\\)

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;

                 \(a_{n}=a*r^{n-1}\)

Where a is first term and r is common ratio.

Given sequence is,

               5, 15, 45, 135

So that, \(a=5,r=15/5=3\)

We have to find 6th term,

                 \(a_{6}=5*3^{6-1} \\\\a_{6}=5*3^{5} \\\\a_{6}=5*243=1215\)

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

Learn more about the geometric sequence here:

https://brainly.com/question/24643676

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