Question

find the $11^{\text{th}}$ term of the following geometric sequence.\
1, 4, 16, 64, ...

Explanation:

Step1: Identify known values

First term $a_1 = 1$, common ratio $r = \frac{4}{1} = 4$, target term $n = 11$

Step2: Use geometric sequence formula

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \times r^{n-1}$

Step3: Substitute values into formula

$a_{11} = 1 \times 4^{11-1} = 4^{10}$

Step4: Calculate the final value

$4^{10} = 1048576$

Answer:

1048576