Find the Next Term -3 , 12 , -48 , 192 , -768

$- 3$ , $12$ , $- 48$ , $192$ , $- 768$

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 $- 4$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 4$

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 $r = - 4$ .

$a_{n} = - 3 {(- 4)}^{n - 1}$

Step 4

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

$a_{6} = - 3 {(- 4)}^{(6) - 1}$

Step 5

Subtract $1$ from $6$ .

$a_{6} = - 3 {(- 4)}^{5}$

Step 6

Raise $- 4$ to the power of $5$ .

$a_{6} = - 3 \cdot - 1024$

Step 7

Multiply $- 3$ by $- 1024$ .

$a_{6} = 3072$

Find the Next Term -3 , 12 , -48 , 192 , -768

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