Identify the Sequence 10 , 9.5 , 9 , 8.5 , 8

$10$ , $9.5$ , $9$ , $8.5$ , $8$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 0.5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 0.5$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 10$ and $d = - 0.5$ .

$a_{n} = 10 - 0.5 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 10 - 0.5 n - 0.5 \cdot - 1$

Multiply $- 0.5$ by $- 1$ .

$a_{n} = 10 - 0.5 n + 0.5$

Step 5

Add $10$ and $0.5$ .

$a_{n} = - 0.5 n + 10.5$

Identify the Sequence 10 , 9.5 , 9 , 8.5 , 8

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