Question

What's the 11th term 5,15,45,135

Answer 1

Answer:

The 11th term is 295,245.

Step-by-step explanation:

We are given the sequence:

$5, 15, 45, 135...$

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:

$x_n=ar^{n-1}$

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:

$x_n=5(3)^{n-1}$

To find the 11th term, substitute 11 for n:

$x_{11}=5(3)^{11-1}$

Evaluate. Thus, the 11th term is:

$x_{11}=5(59049)=295245$