Question

the first three terms of a geometric sequence are as follows.
-256, -64, -16
find the next two terms of this sequence.
give exact values (not decimal approximations).
-256, -64, -16, □,□

Explanation:

Step1: Find common ratio $r$

$r = \frac{\text{second term}}{\text{first term}} = \frac{-64}{-256} = \frac{1}{4}$

Step2: Calculate 4th term

$\text{4th term} = \text{3rd term} \times r = -16 \times \frac{1}{4} = -4$

Step3: Calculate 5th term

$\text{5th term} = \text{4th term} \times r = -4 \times \frac{1}{4} = -1$

Answer:

$-4, -1$