Question

question
find the 12th term of the geometric sequence 2, -4, 8, ...

Explanation:

Step1: Identify common ratio $r$

$r = \frac{-4}{2} = -2$

Step2: Recall nth term formula

The nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1=2$, $n=12$, $r=-2$.

Step3: Substitute values into formula

$a_{12} = 2 \cdot (-2)^{12-1}$

Step4: Simplify the exponent

$a_{12} = 2 \cdot (-2)^{11}$

Step5: Calculate the power and product

$(-2)^{11} = -2048$, so $a_{12} = 2 \cdot (-2048) = -4096$

Answer:

$-4096$