Find the 5th Term 4/3 , 8/3 , 4 , 16/3

$\frac{4}{3}$ , $\frac{8}{3}$ , $4$ , $\frac{16}{3}$

Step 1

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

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

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

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

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

Step 4

Simplify each term.

Apply the distributive property.

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

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

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

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

Combine $\frac{4}{3}$ and $- 1$ .

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

Multiply $4$ by $- 1$ .

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

Move the negative in front of the fraction.

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

Step 5

Combine the opposite terms in $\frac{4}{3} + \frac{4 n}{3} - \frac{4}{3}$ .

Combine the numerators over the common denominator.

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

Subtract $4$ from $4$ .

$a_{n} = \frac{4 n}{3} + \frac{0}{3}$

Divide $0$ by $3$ .

$a_{n} = \frac{4 n}{3} + 0$

Add $\frac{4 n}{3}$ and $0$ .

$a_{n} = \frac{4 n}{3}$

Step 6

Substitute in the value of $n$ to find the $n$ th term.

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

Step 7

Multiply $4$ by $5$ .

$a_{5} = \frac{20}{3}$

Find the 5th Term 4/3 , 8/3 , 4 , 16/3

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