Final answer:
The given sequence 5, -25, 625, -3125 does not have a constant common ratio, switching between -5 and -25. This inconsistency indicates that the sequence is not a geometric sequence.
Step-by-step explanation:
The sequence in question is 5, -25, 625, -3125. To find the common ratio, we divide the second term by the first term, the third term by the second term, and so on to ensure that the ratio is constant.
Dividing the second term (-25) by the first term (5) gives us -5. Dividing the third term (625) by the second term (-25) also gives us -25. Lastly, dividing the fourth term (-3125) by the third term (625) results in -5. It can be seen that the common ratio changes between -5 and -25.
However, upon closer inspection, we realize that this is not a typical geometric sequence because the common ratio is not the same through each pair of terms. In a true geometric sequence, the common ratio must remain constant. Therefore, the given sequence does not have a constant common ratio and is not a geometric sequence.