Algebra Examples

$t_{n} = 2 n^{2} - n$

Step 1

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

$t_{2} = 2 {(2)}^{2} - (2)$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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Step 2.1.1.1

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

$t_{2} = 2 {(2)}^{2} - (2)$

Step 2.1.1.2

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

$t_{2} = 2^{1 + 2} - (2)$

Step 2.1.2

Add $1$ and $2$ .

$t_{2} = 2^{3} - (2)$

Step 2.2

Raise $2$ to the power of $3$ .

$t_{2} = 8 - (2)$

Step 2.3

Multiply $- 1$ by $2$ .

$t_{2} = 8 - 2$

Step 3

Subtract $2$ from $8$ .

$t_{2} = 6$