Question

homework assignment 9.3 geometric sequences
due friday by 11:59pm points 13 submitting an external tool
homework assignment 9.3 geometric sequences
score: 2/13 answered: 2/13
question 3
find a formula for the general term ( a_n ) of the sequence assuming the pattern of the first few terms continues.
( left{ \frac{3}{3}, \frac{3}{9}, \frac{3}{27}, \frac{3}{81}, \frac{3}{243}, dots
ight} )
assume the first term is ( a_1 ).
( a_n = )
question help: video written example

Explanation:

Step1: Identify first term \(a_1\)

First term \(a_1 = \frac{3}{3} = 1\)

Step2: Find common ratio \(r\)

\(r = \frac{a_2}{a_1} = \frac{3/9}{3/3} = \frac{1}{3}\)

Step3: Apply geometric sequence formula

General term: \(a_n = a_1 r^{n-1}\)
Substitute values: \(a_n = 1 \cdot (\frac{1}{3})^{n-1} = \frac{1}{3^{n-1}}\)

Answer:

\(\frac{1}{3^{n-1}}\)