Question

What is the recursive rule for this geometric sequence? 2, 12, 18,  132,  ... Enter your answers in the boxes. an= _ ⋅an−1

Answer 1

The recursive rule for a geometric sequence allow you to find the previous term of an n'th position.

Common Ratio: 6
Recursive Rule Formula: $a_{n+1}=a_{n}*6$

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Answer 2

Answer: $a_{n+1}=6a_n$

Step-by-step explanation:

The given geometric sequence=  2, 12, 18,132,..........

Here the first term $a_1$= 2

The second term $a_2$=12

The third term $a_3$=18

The fourth term $a_4$=132 and so on

We know that the common ratio in geometric series is

$r=\frac{a_{n+1}}{a_n}$

Here, $r=\frac{12}{2}=\frac{18}{12}=\frac{132}{18}=6$

Thus The recursive rule for this geometric sequence is

$6=\frac{a_{n+1}}{a_n}$

$\Rightarrow\ a_{n+1}=6a_n$