Identify the Sequence 0 , 1/2 , 1 , 3/2 , 2

$0$ , $\frac{1}{2}$ , $1$ , $\frac{3}{2}$ , $2$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{1}{2}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{1}{2}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 0$ and $d = \frac{1}{2}$ .

$a_{n} = 0 + \frac{1}{2} (n - 1)$

Step 4

Add $0$ and $\frac{1}{2} (n - 1)$ .

$a_{n} = \frac{1}{2} (n - 1)$

Step 5

Apply the distributive property.

$a_{n} = \frac{1}{2} n + \frac{1}{2} \cdot - 1$

Step 6

Combine $\frac{1}{2}$ and $n$ .

$a_{n} = \frac{n}{2} + \frac{1}{2} \cdot - 1$

Step 7

Combine $\frac{1}{2}$ and $- 1$ .

$a_{n} = \frac{n}{2} + \frac{- 1}{2}$

Step 8

Move the negative in front of the fraction.

$a_{n} = \frac{n}{2} - \frac{1}{2}$

Identify the Sequence 0 , 1/2 , 1 , 3/2 , 2

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