Identify the Sequence 13.1 , 3.1 , -6.9 , -16.9

$13.1$ , $3.1$ , $- 6.9$ , $- 16.9$

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 $a_{1} = 13.1$ and $d = - 10$ .

$a_{n} = 13.1 - 10 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 13.1 - 10 n - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$a_{n} = 13.1 - 10 n + 10$

Step 5

Add $13.1$ and $10$ .

$a_{n} = - 10 n + 23.1$

Identify the Sequence 13.1 , 3.1 , -6.9 , -16.9

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