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) $\dfrac{1}{4}.$

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

$r=\dfrac{a(n+1)}{a(n)},~~~n=0,~1,~2,~~.~~.~~.$

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

$r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.$

We have

$\dfrac{a(2)}{a(1)}=\dfrac{16}{64}=\dfrac{1}{4},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{4}{16}=\dfrac{1}{4},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{1}{4},~~\cdots$

Thus, the required common ratio for the given geometric sequence is $\dfrac{1}{4}.$

Option (C) is CORRECT.