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The given numbers in the sequence projects a geometric sequence with a common ratio of 1/4. This is true because 64 1/4 equals 16 and 16 1/4 equals 4. Furthermore, 4 * 1/4 is equal to 1. hence the answer is 1/4

Answer:  The common ratio for the given sequence is \(\dfrac{1}{4}.\)

Step-by-step explanation:  We are given to find the common ratio for the following sequence:

\(64,~16,~4,~1,~.~.~..\)

We can see that

the given sequence is a geometric sequence with first term, a = 64.

We know that the common ratio 'r' of a geometric sequence will be found by diving each term by its preceding term.

We have

\(\dfrac{16}{64}=\dfrac{4}{16}=\dfrac{1}{4}=~.~.~.~=\dfrac{1}{4}.\)

Thus, the common ratio for the given sequence is \(\dfrac{1}{4}.\)

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