Find the First 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.

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

Step 2

Multiply $\frac{2}{3}$ by $1$ .

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

Step 3

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

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

Step 4

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

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 $\frac{3}{3}$ .

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

Multiply $8$ by $3$ .

$a_{1} = \frac{3}{24} + \frac{2}{3} \cdot \frac{8}{8}$

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$a_{1} = \frac{3}{24} + \frac{2 \cdot 8}{3 \cdot 8}$

Multiply $3$ by $8$ .

$a_{1} = \frac{3}{24} + \frac{2 \cdot 8}{24}$

Step 6

Combine the numerators over the common denominator.

$a_{1} = \frac{3 + 2 \cdot 8}{24}$

Step 7

Simplify the numerator.

Multiply $2$ by $8$ .

$a_{1} = \frac{3 + 16}{24}$

Add $3$ and $16$ .

$a_{1} = \frac{19}{24}$