Question

Identify the next three terms in the geometric sequence.1, 3, 9, 27,..

Answer 1

Given the sequence:

1, 3, 9, 27, ...

Let's identify the next 3 terms in the geometric sequence.

To find the next term, let's first find the common ratio, r, of the sequence.

To find the common ratio, divide a term by the term before it.

We have:

$\begin{gathered} r=\frac{3}{1}=3 \\ \\ r=\frac{9}{3}=3 \\ \\ r=\frac{27}{9}=3 \\ \end{gathered}$

We can see the common ratio between the terms is 3.

Now, to find the next term, multiply the last term by the common ratio.

We have:

Fifth term = fourth term x common ratio = 27 x 3 = 81

Sixth term = fifth term x common ratio = 81 x 3 = 243

Seventh term = sixth term x common ratio = 243 * 3 = 729

Therefore, the next three terms are:

81, 243, and 729

ANSWER:

81, 243, and 729