Find the 4th Term -4 , 8 , -16

$- 4$ , $8$ , $- 16$

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, $a_{n} = a_{1} \cdot r^{n - 1}$ .

Geometric Sequence: $r = - 2$

This is the form of a geometric sequence.

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

Substitute in the values of $a_{1} = - 4$ and $r = - 2$ .

$a_{n} = (- 4) \cdot {(- 2)}^{n - 1}$

Multiply $- 4$ by ${(- 2)}^{n - 1}$ .

$a_{n} = - 4 {(- 2)}^{n - 1}$

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

$a_{4} = - 4 {(- 2)}^{(4) - 1}$

Subtract $1$ from $4$ .

$a_{4} = - 4 {(- 2)}^{3}$

Raise $- 2$ to the power of $3$ .

$a_{4} = - 4 \cdot - 8$

Multiply $- 4$ by $- 8$ .

$a_{4} = 32$

Find the 4th Term -4 , 8 , -16

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