Find the Next Term 3 , -6 , 12 , -24 , 48 , -96 , 192

$3$ , $- 6$ , $12$ , $- 24$ , $48$ , $- 96$ , $192$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $- 2$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 2$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 3$ and $r = - 2$ .

$a_{n} = 3 {(- 2)}^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{8} = 3 {(- 2)}^{(8) - 1}$

Step 5

Subtract $1$ from $8$ .

$a_{8} = 3 {(- 2)}^{7}$

Step 6

Raise $- 2$ to the power of $7$ .

$a_{8} = 3 \cdot - 128$

Step 7

Multiply $3$ by $- 128$ .

$a_{8} = - 384$

Find the Next Term 3 , -6 , 12 , -24 , 48 , -96 , 192

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