Answer :
Final answer:
The common ratio for the given geometric sequence 5, -25, 625, -3125 is -5. You can find it by dividing any term by its previous term. The next term in the sequence would be 15625.
Explanation:
The sequence you've given is a geometric sequence where each term is the product of the previous term and a constant, which is known as the common ratio. To find the common ratio, you can divide any term in the sequence by the term that comes immediately before it.
Step 1: Divide the second term by the first term: -25 ÷ 5 = -5.
Step 2: Check this ratio with another pair of terms to verify if the ratio is consistent: 625 ÷ -25 = -25. So, the ratio seems to be consistent as -5.
Step 3: To find the next term in the sequence, multiply the last term by the common ratio: -3125 × -5 = 15625. Thus, the next term in the sequence is 15625.
The common ratio for this geometric sequence is -5.
