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Answer :
Final answer:
The sequence 100, -50, 25, -12.5, ... is a geometric sequence with a common ratio of -0.5.
Explanation:
The sequence in question is 100, -50, 25, -12.5, .... To determine whether this sequence is geometric or arithmetic, we need to examine the differences or ratios between consecutive terms.
For an arithmetic sequence, the difference between consecutive terms is constant. For example, if we have a sequence like 5, 10, 15, 20, ..., we can see that each term is obtained by adding 5 to the previous term. So, the difference is +5.
For a geometric sequence, the ratio between consecutive terms is constant. Therefore, we divide each term by the previous one to find the common ratio. For the given sequence, dividing the second term by the first term gives -50/100 = -0.5, dividing the third term by the second term gives 25/(-50) = -0.5 again, and so on. This consistent ratio of -0.5 confirms that the sequence is indeed geometric.
Therefore, the sequence 100, -50, 25, -12.5, ... is a geometric sequence with a common ratio of -0.5.
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