Question

1. find the 10th term in the following geometric sequence.

$\frac{1}{3}$, 1, 3, 9...
options: $\frac{246}{3}$, $\frac{82}{3}$, 6561, 19683

Explanation:

Step1: Identify common ratio

$r = \frac{1}{\frac{1}{3}} = 3$

Step2: Recall geometric term formula

$a_n = a_1 \cdot r^{n-1}$

Step3: Substitute known values

$a_{10} = \frac{1}{3} \cdot 3^{10-1}$

Step4: Simplify the expression

$a_{10} = \frac{1}{3} \cdot 3^9 = 3^8 = 6561$

Answer:

C. 6561