Identify the Sequence 5/4 , 1/2 , -1/4 , -1 , -7/4

$\frac{5}{4}$ , $\frac{1}{2}$ , $- \frac{1}{4}$ , $- 1$ , $- \frac{7}{4}$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- \frac{3}{4}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - \frac{3}{4}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{5}{4}$ and $d = - \frac{3}{4}$ .

$a_{n} = \frac{5}{4} - \frac{3}{4} (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = \frac{5}{4} - \frac{3}{4} n - \frac{3}{4} \cdot - 1$

Combine $n$ and $\frac{3}{4}$ .

$a_{n} = \frac{5}{4} - \frac{n \cdot 3}{4} - \frac{3}{4} \cdot - 1$

Multiply $- \frac{3}{4} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$a_{n} = \frac{5}{4} - \frac{n \cdot 3}{4} + 1 (\frac{3}{4})$

Multiply $\frac{3}{4}$ by $1$ .

$a_{n} = \frac{5}{4} - \frac{n \cdot 3}{4} + \frac{3}{4}$

Move $3$ to the left of $n$ .

$a_{n} = \frac{5}{4} - \frac{3 n}{4} + \frac{3}{4}$

Step 5

Combine the numerators over the common denominator.

$a_{n} = \frac{5 - 3 n + 3}{4}$

Step 6

Add $5$ and $3$ .

$a_{n} = \frac{- 3 n + 8}{4}$

Identify the Sequence 5/4 , 1/2 , -1/4 , -1 , -7/4

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