Identify the Sequence 7 , 16 , 25 , 34

$7$ , $16$ , $25$ , $34$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $9$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 9$

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 $d = 9$ .

$a_{n} = 7 + 9 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 7 + 9 n + 9 \cdot - 1$

Multiply $9$ by $- 1$ .

$a_{n} = 7 + 9 n - 9$

Step 5

Subtract $9$ from $7$ .

$a_{n} = 9 n - 2$

Identify the Sequence 7 , 16 , 25 , 34

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