Identify the Sequence -5 , 13 , 31 , 49

$- 5$ , $13$ , $31$ , $49$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $18$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 18$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - 5$ and $d = 18$ .

$a_{n} = - 5 + 18 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 5 + 18 n + 18 \cdot - 1$

Multiply $18$ by $- 1$ .

$a_{n} = - 5 + 18 n - 18$

Step 5

Subtract $18$ from $- 5$ .

$a_{n} = 18 n - 23$

Identify the Sequence -5 , 13 , 31 , 49

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