Question

find the $10^{\text{th}}$ term of the following geometric sequence.\
7, 21, 63, 189, ...

Explanation:

Step1: Identify first term $a_1$

$a_1 = 7$

Step2: Calculate common ratio $r$

$r = \frac{21}{7} = 3$

Step3: Use geometric term formula

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \times r^{n-1}$. For $n=10$:
$a_{10} = 7 \times 3^{10-1} = 7 \times 3^9$

Step4: Compute $3^9$ and multiply

$3^9 = 19683$, so $a_{10} = 7 \times 19683 = 137781$

Answer:

137781