im doing my summer homework & im a little confused on this one...please help me...
What is the next term in the geometic series 16,-4,1,-1/4,.....
a. -1/8
b.0
c.1/16
d.1/8
e.1/2
To find the next term in a geometric series, you need to determine the common ratio between consecutive terms. Once you have the common ratio, you can apply it to calculate the missing term.
In this series, each term is obtained by multiplying the previous term by the same constant factor. Let's examine the ratios between consecutive terms:
-4/16 = -1/4
1/-4 = -1/4
-1/4 / 1 = -1/4
We can see that the common ratio between terms is -1/4 because we obtain the same value (-1/4) each time we divide a term by its preceding term.
To find the next term, multiply the last term, -1/4, by the common ratio (-1/4):
(-1/4) * (-1/4) = 1/16
Therefore, the next term in the series is 1/16.
So, the correct answer is c. 1/16.