Question

find the sum of \\(81, 27, 9, 3, \dots\\).

\\(\text{sum} = \\)

Explanation:

Step1: Identify the first term and common ratio

$$a = 81, \quad r = \frac{27}{81} = \frac{1}{3}$$

Step2: Apply the infinite geometric series formula

$$S = \frac{a}{1 - r} = \frac{81}{1 - \frac{1}{3}}$$

Step3: Calculate the sum

$$S = \frac{81}{\frac{2}{3}} = \frac{243}{2} = 121.5$$

Answer:

\(121.5\) (or \(\frac{243}{2}\))