Find the First Term a_n=72(1/3)^(n-1)

$a_{n} = 72 {(\frac{1}{3})}^{n - 1}$

Step 1

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

$a_{1} = 72 {(\frac{1}{3})}^{(1) - 1}$

Step 2

Simplify the expression.

Subtract $1$ from $1$ .

$a_{1} = 72 {(\frac{1}{3})}^{0}$

Apply the product rule to $\frac{1}{3}$ .

$a_{1} = 72 (\frac{1^{0}}{3^{0}})$

Anything raised to $0$ is $1$ .

$a_{1} = 72 (\frac{1}{3^{0}})$

Anything raised to $0$ is $1$ .

$a_{1} = 72 (\frac{1}{1})$

Step 3

Cancel the common factor of $1$ .

Cancel the common factor.

$a_{1} = 72 (\frac{1}{1})$

Rewrite the expression.

$a_{1} = 72 \cdot 1$

Step 4

Multiply $72$ by $1$ .

$a_{1} = 72$