Question

What is the common ratio of 64, 16, 4, 1?

Answer 1

Answer: The common ratio for the given sequence is
`(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

`(16)/(64)=(4)/(16)=(1)/(4)=~.~.~.~=(1)/(4).`

Thus, the common ratio for the given sequence is
`(1)/(4).`

Answer 2

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