Question

find the fourth term of the geometric sequence, given the first term and common ratio.\\(a_1 = 8\\) and \\(r = 4\\)\\(a_4 = ?\\)

Explanation:

Step1: Recall geometric sequence formula

The nth term of a geometric sequence is given by $a_n = a_1 \times r^{n-1}$

Step2: Substitute given values

For $n=4$, $a_1=8$, $r=4$:
$a_4 = 8 \times 4^{4-1}$

Step3: Simplify the exponent

$4^{4-1}=4^3=64$

Step4: Calculate the final value

$a_4 = 8 \times 64$

Answer:

512