find the 7th term in the sequence 2, 8, 32, 128, . . . hint: write a formula to help you. 1st term · common…

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1 = 2$. To find the common ratio $r$, divide the second term by the first term: $r=\frac{8}{2}=4$.

Step2: Use the formula for the $n$th term of a geometric sequence

The formula for the $n$th term of a geometric sequence is $a_n=a_1\cdot r^{(n - 1)}$. We want to find the 7th term, so $n = 7$, $a_1 = 2$, and $r = 4$. Substitute these values into the formula: $a_7=2\times4^{(7 - 1)}$.

Step3: Calculate the value of $4^6$

$4^6=4\times4\times4\times4\times4\times4 = 4096$.

Step4: Calculate the 7th term

$a_7=2\times4096=8192$.

Answer:

$8192$