Identify the Sequence -51 , -34 , -17 , 0

$- 51$ , $- 34$ , $- 17$ , $0$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $17$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 17$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - 51$ and $d = 17$ .

$a_{n} = - 51 + 17 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 51 + 17 n + 17 \cdot - 1$

Multiply $17$ by $- 1$ .

$a_{n} = - 51 + 17 n - 17$

Step 5

Subtract $17$ from $- 51$ .

$a_{n} = 17 n - 68$

Identify the Sequence -51 , -34 , -17 , 0

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