Answer: To find the recursive formula for a geometric sequence, we need to use the fact that each term is equal to the previous term multiplied by a common ratio, r.
In this case, the first term is a1 = 125 and the common ratio is r = 1/5. Therefore, the second term is a2 = a1 x r = 125 x 1/5 = 25, the third term is a3 = a2 x r = 25 x 1/5 = 5, and so on.
The recursive formula for a geometric sequence is:
a1 = 125
an = an-1 x (1/5)
So, the recursive formula for this sequence is:
a1 = 125
a2 = a1 x (1/5) = 25
a3 = a2 x (1/5) = 5
a4 = a3 x (1/5) = 1
and so on.
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Step-by-step explanation: