Precalculus Examples

$1$ , $4$ , $7$ , $10$ , $13$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $3$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 3$

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 $d = 3$ .

$a_{n} = 1 + 3 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 1 + 3 n + 3 \cdot - 1$

Step 4.2

Multiply $3$ by $- 1$ .

$a_{n} = 1 + 3 n - 3$

Step 5

Subtract $3$ from $1$ .

$a_{n} = 3 n - 2$

Step 6

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

$a_{6} = 3 (6) - 2$

Step 7

Multiply $3$ by $6$ .

$a_{6} = 18 - 2$

Step 8

Subtract $2$ from $18$ .

$a_{6} = 16$