Identify the Sequence 11 , 8.5 , 6 , 3.5 , 1

$11$ , $8.5$ , $6$ , $3.5$ , $1$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 2.5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 2.5$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 11$ and $d = - 2.5$ .

$a_{n} = 11 - 2.5 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 11 - 2.5 n - 2.5 \cdot - 1$

Multiply $- 2.5$ by $- 1$ .

$a_{n} = 11 - 2.5 n + 2.5$

Step 5

Add $11$ and $2.5$ .

$a_{n} = - 2.5 n + 13.5$

Identify the Sequence 11 , 8.5 , 6 , 3.5 , 1

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