Question

Which formula can be used to describe the sequence below 27,9,3​

Answer 1

Answer:

$a_n=27 \cdot (\frac{1}{3})^{n-1}$.

Step-by-step explanation:

This is a geometric sequence that means there is a common ratio.  That means there is a number you can multiply over and over to get the next term.

The first term is 27.

The second term is (1/3)(27)=9.

The third term is (1/3)(9)=3.

So the common ratio is 1/3.

That means you can keep multiplying by 1/3 to find the next term in the sequence.

The explicit form for a geometric sequence is $a_n=a_1 \cdot r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio.

We are given $a_1=27$ and $r=\frac{1}{3}$.

So the explicit form for the given sequence is $a_n=27 \cdot (\frac{1}{3})^{n-1}$.