Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.

Question

asked Aug 16, 2023 3.5k views

1 Answer

Esko · Answer 1 · 2023-08-22T09:43:15+0000

Solution:

Given the sequence;

The common ratio is the ratio between two consecutive numbers in a geometric sequence.

Thus;

$\begin{gathered} r=(a_2)/(a_1)=(a_3)/(a_2) \\ \\ r=(6)/(-3) \\ \\ r=-2 \end{gathered}$

Common Ratio:

Also, given the formula;

$a_n=-3\cdot(-2)^(n-1)$

The formula is an explicit formula of the geometric sequence.

The recursive formula is;

$\begin{gathered} a_n=r(a_(n-1)) \\ \\ a_n=-2(a_(n-1)) \end{gathered}$

Then, the ninth term is;

$\begin{gathered} n=9 \\ \\ a_9=-3\cdot(-2)^(9-1) \\ \\ a_9=-3\cdot(-2)^8 \\ \\ a_9=-3(256) \\ \\ a_9=-768 \end{gathered}$

The ninth term is;