Identify the Sequence 6 , 10 , 14 , __

Explanation

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $4$ to the previous term in the sequence gives the next term. In other words, $�_{�} = �_{1} + � (� - 1)$ .

Arithmetic Sequence: $� = 4$

This is the formula of an arithmetic sequence.

$�_{�} = �_{1} + � (� - 1)$

Substitute in the values of $�_{1} = 6$ and $� = 4$ .

$�_{�} = 6 + 4 (� - 1)$

Simplify each term.

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$�_{�} = 6 + 4 � - 4$

Subtract $4$ from $6$ .

$a n = 4 n + 2 " role="presentation" style="outline: 0px; display: inline-block; line-height: 0; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"> a_{n} = 4 n + 2$