Answer:
- geometric
- common ratio: -5
- a[n]=-5a[n-1]; 625
Explanation:
A.
We start this problem the way we start all problems: we read the problem statement and observe the given data and relationships.
Here, we observe that the given numbers are all multiples (powers) of 5, with alternating signs. We know that an arithmetic sequence cannot have alternating signs, so this is not an arithmetic sequence.
We are familiar with the first few powers of 5, so we recognize the terms have a common ratio of -5. If terms have a common ratio, they are a geometric sequence, so this is a geometric sequence.
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B.
As we observed in Part A, the common ratio is -5.
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C.
The full recursive formula will include the initial value in the sequence:
a[1] = -5
a[n] = -5·a[n-1]
Then the next value is ...
a[4] = -5·a[3] = -5·(-125)
a[4] = 625