Question

The first term of a geometric sequence is –2 and the common -1/4. What are the next three terms of the sequence?

Answer 1

`a_1=-2\\ a_2=-2\cdot\left(-(1)/(4)\right)=(1)/(2)\\ a_3=-2\cdot\left(-(1)/(4)\right)^2=-(1)/(8)\\ a_4=-2\cdot\left(-(1)/(4)\right)^3=(1)/(32)`

Answer 2

The common ratio tells you by which factor every successive term will be with respect to the preceding term so you have:

-2(-1/4)(-1/4)(-1/4)

1/2, -1/8, 1/32