Question

6.6 comparing linear and exponential functions (sequences) quiz

find the next term in the geometric sequence: 6, 18, 54,

Explanation:

Identify the sequence type

Using the Geometric Sequences knowledge point
The given sequence is \(6, 18, 54, \dots\), which is explicitly stated to be geometric.

Determine the common ratio

Using the Common Ratio knowledge point

$$ r = \frac{18}{6} = 3 $$

$$ r = \frac{54}{18} = 3 $$

Calculate the next term

Using the Geometric Sequences knowledge point

$$ a_4 = 54 \times 3 = 162 $$

Answer:

Find the next term in the geometric sequence: 6, 18, 54, <blank>162</blank>