Question

What is the common ratio for this geometric sequence?

Answer 1

Answer is c 1/4 and yes it is the true answer

Answer 2

Answer: The correct option is (C)
`(1)/(4).`

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

64, 16, 4, 1, . . .

We know that

if a(n) represents the n-th term of a geometric series, then the common ratio is given by

`r=(a(n+1))/(a(n)),~~~n=0,~1,~2,~~.~~.~~.`

For the given geometric sequence, we have

a(1) = 64, a(2) = 16, a(3) = 4, a(4) = 1, . . .

So, the common ratio r will be given by

`r=(a(2))/(a(1))=(a(3))/(a(2))=(a(4))/(a(3))=~~.~~.~~.`

We have

`(a(2))/(a(1))=(16)/(64)=(1)/(4),\\\\\\(a(3))/(a(2))=(4)/(16)=(1)/(4),\\\\\\(a(4))/(a(3))=(1)/(4),~~\cdots`

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

Option (C) is CORRECT.