Identify the Progression -2 , 4 , -8 , 16 , -32

$- 2$ , $4$ , $- 8$ , $16$ , $- 32$

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 $a_{1} = - 2$ and $r = - 2$ .

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

Step 4

Multiply $- 2$ by ${(- 2)}^{n - 1}$ by adding the exponents.

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

Raise $- 2$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Combine the opposite terms in $1 + n - 1$ .

Subtract $1$ from $1$ .

$a_{n} = {(- 2)}^{n + 0}$

Add $n$ and $0$ .

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

Identify the Progression -2 , 4 , -8 , 16 , -32

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