Mathematics: Correct answer only ! enter a recursive rule for the geometric sequence. 6, − 18, 54, − 162,

Correct answer only ! enter a recursive rule for

dearydn22

10.03.2022

$\bold{a_1=6,\quad a_n=-3a_{n-1}}$

Step-by-step explanation:

The recursive rule for a general geometric sequence is: $a_n=a_{n-1}(r)\quad \text{where}\ a_{n-1}\ \text{is the previous term and r is the ratio}$

Given the sequence {6. -18, 54, -162, ... }, we can see that

$\text{the first term}\ (a_1)\ \text{is 6}$ $\text{the common ratio (r) is:}\ \dfrac{-18}{6}=-3$

So, the recursive rule is: $a_n=-3a_{n-1}$

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