Identify the Sequence 54 , 63 , 72 , 81

$54$ , $63$ , $72$ , $81$

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 $a_{1} = 54$ and $d = 9$ .

$a_{n} = 54 + 9 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 54 + 9 n + 9 \cdot - 1$

Multiply $9$ by $- 1$ .

$a_{n} = 54 + 9 n - 9$

Step 5

Subtract $9$ from $54$ .

$a_{n} = 9 n + 45$

Identify the Sequence 54 , 63 , 72 , 81

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