Answer :
Final answer:
The given sequence is a geometric sequence, where each term is a fifth of the preceding term. The common ratio of the sequence is therefore 1/5. The next term in the sequence can be found by multiplying the last given number by this common ratio, which gives us 125.
Explanation:
The given sequence is 78125, 15625, 3125, 625. From these numbers, it can be observed that each term in the sequence is a fifth of the preceding term. Specifically, if you divide 78125 by 5, you get 15625. If you divide 15625 by 5, you get 3125. Finally, when you divide 3125 by 5, you obtain 625. Hence, this is a geometric sequence with the common ratio of 1/5.
Geometric sequences are sequences where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 1/5. Hence, to find the next number in the sequence, you just need to multiply the last given number (which is 625) by 1/5.
So, the next number in the sequence would be 625 * (1/5) = 125.
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