Question

find the sixth term of the geometric sequence, given the first term and common ratio.\\(a_1 = 100\\) and \\(r = 2\\)\\(a_6 = ?\\)

Explanation:

Step1: Recall nth term formula

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

Step2: Substitute given values

Substitute $a_1=100$, $r=2$, $n=6$ into the formula:
$a_6 = 100 \times 2^{6-1}$

Step3: Simplify the exponent

Calculate the exponent first:
$2^{6-1}=2^5=32$

Step4: Compute the final value

Multiply the first term by the result:
$a_6 = 100 \times 32$

Answer:

3200