Algebra Examples

$3 n^{2} - 1$

Step 1

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

$a_{3} = 3 {(3)}^{2} - 1$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by ${(3)}^{2}$ by adding the exponents.

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Step 2.1.1

Multiply $3$ by ${(3)}^{2}$ .

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Step 2.1.1.1

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

$a_{3} = 3 {(3)}^{2} - 1$

Step 2.1.1.2

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

$a_{3} = 3^{1 + 2} - 1$

Step 2.1.2

Add $1$ and $2$ .

$a_{3} = 3^{3} - 1$

Step 2.2

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

$a_{3} = 27 - 1$

Step 3

Subtract $1$ from $27$ .

$a_{3} = 26$