Precalculus Examples

$- 31$ , $- 41$ , $- 51$ , $- 61$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 10$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 10$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - 31$ and $d = - 10$ .

$a_{n} = - 31 - 10 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = - 31 - 10 n - 10 \cdot - 1$

Step 4.2

Multiply $- 10$ by $- 1$ .

$a_{n} = - 31 - 10 n + 10$

Step 5

Add $- 31$ and $10$ .

$a_{n} = - 10 n - 21$

Step 6

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

$a_{5} = - 10 \cdot 5 - 21$

Step 7

Multiply $- 10$ by $5$ .

$a_{5} = - 50 - 21$

Step 8

Subtract $21$ from $- 50$ .

$a_{5} = - 71$