What are the next three terms of the geometric sequence 32, -16, 8, …?
To find the next three terms of a geometric sequence, we need to identify the common ratio and then continue the pattern by multiplying each term by the common ratio.
In this sequence, the common ratio can be found by dividing any term by its previous term. Let's take the second term and divide it by the first term:
-16 / 32 = -0.5
So the common ratio for this geometric sequence is -0.5.
Now, to find the next term, we multiply the previous term by the common ratio (-0.5):
8 * (-0.5) = -4
To find the term after that, we multiply the previous term (-4) by the common ratio (-0.5):
-4 * (-0.5) = 2
And finally, to find the term after that, we multiply the previous term (2) by the common ratio (-0.5):
2 * (-0.5) = -1
Therefore, the next three terms of the geometric sequence 32, -16, 8, … are -4, 2, and -1.