Answer :
Answer:
The 11th term is 295,245.
Step-by-step explanation:
We are given the sequence:
[tex]5, 15, 45, 135...[/tex]
And we want to find the 11th term.
First, let's determine whether this is an arithmetic sequence or a geometric sequence.
Arithmetic sequences have common differences, while geometric sequences have common ratios.
We can determine that our sequence is a geometric sequence because each subsequent term is triple the previous term: our common ratio is 3.
To find the 11th term, we can write an explicit formula for our sequence. The explicit formula for a geometric sequence is given by:
[tex]x_n=ar^{n-1}[/tex]
Where a is the initial term, r is the common ratio, and n is the nth term.
Since initial term is 5, and the common ratio is 3. Thus:
[tex]x_n=5(3)^{n-1}[/tex]
To find the 11th term, substitute 11 for n:
[tex]x_{11}=5(3)^{11-1}[/tex]
Evaluate. Thus, the 11th term is:
[tex]x_{11}=5(59049)=295245[/tex]