Precalculus Examples

$70$ , $65$ , $60$ , $55$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 5$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 70$ and $d = - 5$ .

$a_{n} = 70 - 5 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 70 - 5 n - 5 \cdot - 1$

Step 4.2

Multiply $- 5$ by $- 1$ .

$a_{n} = 70 - 5 n + 5$

Step 5

Add $70$ and $5$ .

$a_{n} = - 5 n + 75$

Step 6

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

$a_{5} = - 5 \cdot 5 + 75$

Step 7

Multiply $- 5$ by $5$ .

$a_{5} = - 25 + 75$

Step 8

Add $- 25$ and $75$ .

$a_{5} = 50$