Solve for a7 a_7=6(-1/2)^(7-1)

$a_{7} = 6 {(- \frac{1}{2})}^{7 - 1}$

Step 1

Subtract $1$ from $7$ .

$a_{7} = 6 {(- \frac{1}{2})}^{6}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{1}{2}$ .

$a_{7} = 6 ({(- 1)}^{6} {(\frac{1}{2})}^{6})$

Apply the product rule to $\frac{1}{2}$ .

$a_{7} = 6 ({(- 1)}^{6} \frac{1^{6}}{2^{6}})$

$a_{7} = 6 ({(- 1)}^{6} \frac{1^{6}}{2^{6}})$

Step 3

Simplify the expression.

Raise $- 1$ to the power of $6$ .

$a_{7} = 6 (1 \frac{1^{6}}{2^{6}})$

Multiply $\frac{1^{6}}{2^{6}}$ by $1$ .

$a_{7} = 6 \frac{1^{6}}{2^{6}}$

One to any power is one.

$a_{7} = 6 \frac{1}{2^{6}}$

Raise $2$ to the power of $6$ .

$a_{7} = 6 (\frac{1}{64})$

$a_{7} = 6 (\frac{1}{64})$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$a_{7} = 2 (3) \frac{1}{64}$

Factor $2$ out of $64$ .

$a_{7} = 2 \cdot 3 \frac{1}{2 \cdot 32}$

Cancel the common factor.

$a_{7} = 2 \cdot 3 \frac{1}{2 \cdot 32}$

Rewrite the expression.

$a_{7} = 3 (\frac{1}{32})$

$a_{7} = 3 (\frac{1}{32})$

Step 5

Combine $3$ and $\frac{1}{32}$ .

$a_{7} = \frac{3}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a_{7} = \frac{3}{32}$

Decimal Form:

$a_{7} = 0.09375$

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