Question

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

Answer 1

The 11th term is 295,245.

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`