the first three terms of a geometric sequence are as follows.
-4, 20, -100
find the next two terms of this sequence.
give exact values (not decimal approximations).

-4, 20, -100, 500, -2500

Step-by-step explanation:

Since this is a geometric sequence, you know that to get from one term to the next, you must multiply the previous term by a constant value. To find this constant value, known as the constant ratio, divide a term by the consecutive previous term (the term right before it). For this sequence, we can divide the second term, 20, by the first, -4, to get a constant ratio of -5. Now we know that to get from one term to the next, you multiply the previous term by -5. Now, apply this to the question: if you have -100 and need to find the next two terms, multiply -100 by -5 to get the fourth term, 500, and multiply that by -5 again to get your fifth term, -2500. So, your next two terms of this sequence are 500 and -2500, making the sequence -4, 20, -100, 500, -2500, and so on.