Question

The first three terms of a geometric sequence are as follows.

-3, 15, -75
Find the next two terms of this sequence.
Give exact values (not decimal approximations).

Answer 1

To find the next two terms of the geometric sequence, divide any term by its previous term to determine the common ratio. The next term can be found by multiplying the previous term by the common ratio.

Step-by-step explanation:

To find the next two terms of the geometric sequence, we need to determine the common ratio. The common ratio can be found by dividing any term in the sequence by its previous term. In this case, we can divide 15 by -3 to get the common ratio of -5.

Using this common ratio, we can find the next term by multiplying the previous term by the common ratio. So, the fourth term is -75 * -5 = 375. Similarly, the fifth term can be found by multiplying the fourth term by the common ratio, which gives us 375 * -5 = -1875.

Therefore, the next two terms of the sequence are 375 and -1875.