Find the Second Term a_n=1/8+2/3n

$a_{n} = \frac{1}{8} + \frac{2}{3} n$

Step 1

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

$a_{2} = \frac{1}{8} + \frac{2}{3} \cdot (2)$

Step 2

Multiply $\frac{2}{3} (2)$ .

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

$a_{2} = \frac{1}{8} + \frac{2 \cdot 2}{3}$

Multiply $2$ by $2$ .

$a_{2} = \frac{1}{8} + \frac{4}{3}$

Step 3

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a_{2} = \frac{1}{8} \cdot \frac{3}{3} + \frac{4}{3}$

Step 4

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$a_{2} = \frac{1}{8} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{8}{8}$

Step 5

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$a_{2} = \frac{3}{8 \cdot 3} + \frac{4}{3} \cdot \frac{8}{8}$

Multiply $8$ by $3$ .

$a_{2} = \frac{3}{24} + \frac{4}{3} \cdot \frac{8}{8}$

Multiply $\frac{4}{3}$ by $\frac{8}{8}$ .

$a_{2} = \frac{3}{24} + \frac{4 \cdot 8}{3 \cdot 8}$

Multiply $3$ by $8$ .

$a_{2} = \frac{3}{24} + \frac{4 \cdot 8}{24}$

Step 6

Combine the numerators over the common denominator.

$a_{2} = \frac{3 + 4 \cdot 8}{24}$

Step 7

Simplify the numerator.

Multiply $4$ by $8$ .

$a_{2} = \frac{3 + 32}{24}$

Add $3$ and $32$ .

$a_{2} = \frac{35}{24}$