Finite Math Examples

$3 \cdot \frac{3^{n - 1} - 1}{2} + 1$

Step 1

Combine into one fraction.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{3 (3^{n - 1} - 1)}{2} + \frac{2}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 (3^{n - 1} - 1) + 2}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{3 \cdot 3^{n - 1} + 3 \cdot - 1 + 2}{2}$

Step 2.2

Multiply $3$ by $3^{n - 1}$ by adding the exponents.

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Step 2.2.1

Multiply $3$ by $3^{n - 1}$ .

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Step 2.2.1.1

Raise $3$ to the power of $1$ .

$\frac{3^{1} \cdot 3^{n - 1} + 3 \cdot - 1 + 2}{2}$

Step 2.2.1.2

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

$\frac{3^{1 + n - 1} + 3 \cdot - 1 + 2}{2}$

Step 2.2.2

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

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Step 2.2.2.1

Subtract $1$ from $1$ .

$\frac{3^{n + 0} + 3 \cdot - 1 + 2}{2}$

Step 2.2.2.2

Add $n$ and $0$ .

$\frac{3^{n} + 3 \cdot - 1 + 2}{2}$

Step 2.3

Multiply $3$ by $- 1$ .

$\frac{3^{n} - 3 + 2}{2}$

Step 2.4

Add $- 3$ and $2$ .

$\frac{3^{n} - 1}{2}$