Identify the Sequence 1/2 , 2 , 7/2 , 5

$\frac{1}{2}$ , $2$ , $\frac{7}{2}$ , $5$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{3}{2}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{3}{2}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{1}{2}$ and $d = \frac{3}{2}$ .

$a_{n} = \frac{1}{2} + \frac{3}{2} (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = \frac{1}{2} + \frac{3}{2} n + \frac{3}{2} \cdot - 1$

Combine $\frac{3}{2}$ and $n$ .

$a_{n} = \frac{1}{2} + \frac{3 n}{2} + \frac{3}{2} \cdot - 1$

Multiply $\frac{3}{2} \cdot - 1$ .

Combine $\frac{3}{2}$ and $- 1$ .

$a_{n} = \frac{1}{2} + \frac{3 n}{2} + \frac{3 \cdot - 1}{2}$

Multiply $3$ by $- 1$ .

$a_{n} = \frac{1}{2} + \frac{3 n}{2} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$a_{n} = \frac{1}{2} + \frac{3 n}{2} - \frac{3}{2}$

Step 5

Combine the numerators over the common denominator.

$a_{n} = \frac{1 + 3 n - 3}{2}$

Step 6

Subtract $3$ from $1$ .

$a_{n} = \frac{3 n - 2}{2}$

Identify the Sequence 1/2 , 2 , 7/2 , 5

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