The first four terms of a geometric sequence are shown below, where $$ a_{1}=-3 $$. $$ -3,-9,-27,-81 $$ Based on that information, choose the equation that can be used to find the $$ n^{\text {th }} $$ term in the sequence, $$ a_{n} $$. Need some help? View the tips for success! $$ a_{n}=-1(3)^{n} $$ $$ a_{n 2}=-3(3)^{n} $$ $$ a_{n}=-3(-3)^{n} $$ $$ a_{n}=-1\left(\frac{1}{3}\right)^{\pi} $$

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UpStudy AI · Accepted Answer

Given that the sequence is geometric with first term

$$
a_1 = -3,
$$

we first find the common ratio $$ r $$ by dividing the second term by the first term:

$$
r = \frac{-9}{-3} = 3.
$$

For a geometric sequence, the $$ n^{\text{th}} $$ term is given by

$$
a_n = a_1 \cdot r^{n-1}.
$$

Substitute $$ a_1 = -3 $$ and $$ r = 3 $$:

$$
a_n = -3 \cdot 3^{n-1}.
$$

This expression can be rewritten as

$$
a_n = -3^{n},
$$

since

$$
-3^{n} = -3 \cdot 3^{n-1}.
$$

Comparing with the provided options, the equation

$$
a_{n} = -1(3)^{n}
$$

matches the derived formula.
The equation to find the $$ n^{\text{th}} $$ term is $$ a_{n} = -1(3)^{n} $$.

The first four terms of a geometric sequence are shown below, where .

Based on that information, choose the equation that can be used to find the term in the sequence, .

Need some help? View the tips for success!

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The first four terms of a geometric sequence are shown below, where . Based on that information, choose the equation that can be used to find the term in the sequence, . Need some help? View the tips for success!