Precalculus Examples

1

$1$ ,

$3$ ,

$5$ ,

$7$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

$2$ to the previous term in the sequence gives the next term. In other words,

$a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence:

$d = 2$

Step 2

This is the formula of an arithmetic sequence.

$a_{n} = a_{1} + d (n - 1)$

Step 3

Substitute in the values of

$a_{1} = 1$ and

$d = 2$ .

$a_{n} = 1 + 2 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 1 + 2 n + 2 \cdot - 1$

Step 4.2

Multiply

$2$ by

$- 1$ .

$a_{n} = 1 + 2 n - 2$

Step 5

Subtract

$2$ from

$1$ .

$a_{n} = 2 n - 1$

$1, 3, 5, 7$

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