The formula of the $$ n $$th term of the sequence $$ 3,-6,12,-24,48 \ldots $$ is 1) $$ a_{n}=-2(3)^{n} $$ 3) $$ a_{n}=-2(3)^{n-1} $$ 2) $$ a_{n}=3(-2)^{n} $$ 4) $$ a_{n}=3(-2)^{n-1} $$ Option 1 Option 2 Option 3 Option 4

Question

UpStudy AI · Accepted Answer

The sequence is given by:
$$
3, \quad -6, \quad 12, \quad -24, \quad 48, \ldots
$$

**Step 1.** Determine the common ratio by dividing the second term by the first term:
$$
\text{Common ratio } r = \frac{-6}{3} = -2.
$$

**Step 2.** Confirm the ratio with subsequent terms:
$$
\frac{12}{-6} = -2, \qquad \frac{-24}{12} = -2.
$$
Thus, the sequence is geometric with common ratio $$ r = -2 $$.

**Step 3.** The formula for the $$ n $$th term of a geometric sequence is:
$$
a_n = a_1 \cdot r^{n-1}.
$$
Here, $$ a_1 = 3 $$ and $$ r = -2 $$.

**Step 4.** Substitute the values into the formula:
$$
a_n = 3(-2)^{n-1}.
$$

Comparing with the given options, the correct answer is:

Option 4
The $$ n $$th term of the sequence is $$ a_{n} = 3(-2)^{n-1} $$, so the correct option is Option 4.

The formula of the \( n \)th term of the sequence \( 3,-6,12,-24,48 \ldots \) is 1) \( a_{n}=-2(3)^{n} \) 3) \( a_{n}=-2(3)^{n-1} \) 2) \( a_{n}=3(-2)^{n} \) 4) \( a_{n}=3(-2)^{n-1} \) Option 1 Option 2 Option 3 Option 4

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Algebra Questions