Identify the Sequence -7 , 3 , 13 , 23

$- 7$ , $3$ , $13$ , $23$

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 $a_{1} = - 7$ and $d = 10$ .

$a_{n} = - 7 + 10 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 7 + 10 n + 10 \cdot - 1$

Multiply $10$ by $- 1$ .

$a_{n} = - 7 + 10 n - 10$

Step 5

Subtract $10$ from $- 7$ .

$a_{n} = 10 n - 17$

Identify the Sequence -7 , 3 , 13 , 23

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