Question

The first 4 terms of a geometric sequence are 2, 6, 18, 54. Part A: Find the common ratio. Remember the common ratio is the number that is multiplied to each value to get the next number. Part B: Find the next 3 values in the geometric sequence Come up with your own geometric sequence and identify the common ratio.

Answer 1

Common ratio is 3

The three terms are 162, 486, 1458

Explanation:

Given: The first 4 terms of a sequence are
`2,6,18,54`

To find:

A. the common ratio

B. the next 3 values in the geometric sequence

Solution:

Geometric sequence is a sequence in which each of the terms is obtained by multiplying the previous term by a fixed number.

A.

`(6)/(2)=3\\\\(18)/(6)=3\\\\(54)/(18)=3`

So, the common ratio is
`3`

B.

The next three values are as follows:

`54(3)=162\\162(3)=486\\486(3)=1458`