Precalculus Examples

$a \cdot 1 = 2$ , $a (n) = 3 a (n - 1) - 1$

Step 1

Multiply $a$ by $1$ .

$a = 2$

Step 2

Replace all occurrences of $a$ with $2$ in each equation.

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Step 2.1

Replace all occurrences of $a$ in $a (n) = 3 a (n - 1) - 1$ with $2$ .

$(2) (n) = 3 (2) (n - 1) - 1$

$a = 2$

Step 2.2

Simplify $(2) (n) = 3 (2) (n - 1) - 1$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Multiply $2$ by $n$ .

$2 n = 3 (2) (n - 1) - 1$

$a = 2$

$2 n = 3 (2) (n - 1) - 1$

$a = 2$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $3 (2) (n - 1) - 1$ .

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Step 2.2.2.1.1

Simplify each term.

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Step 2.2.2.1.1.1

Multiply $3$ by $2$ .

$2 n = 6 (n - 1) - 1$

$a = 2$

Step 2.2.2.1.1.2

Apply the distributive property.

$2 n = 6 n + 6 \cdot - 1 - 1$

$a = 2$

Step 2.2.2.1.1.3

Multiply $6$ by $- 1$ .

$2 n = 6 n - 6 - 1$

$a = 2$

$2 n = 6 n - 6 - 1$

$a = 2$

Step 2.2.2.1.2

Subtract $1$ from $- 6$ .

$2 n = 6 n - 7$

$a = 2$

$2 n = 6 n - 7$

$a = 2$

$2 n = 6 n - 7$

$a = 2$

$2 n = 6 n - 7$

$a = 2$

$2 n = 6 n - 7$

$a = 2$

Step 3

Reduce the system.

$n = \frac{7}{4}, a = 2$