QuestionFind the common ratio of the geometric sequence: $64, 16, 4, 1, \ldots$ . A. 4 B. $\frac{1}{4}$ C. 8 D. $\frac{1}{8}$

Studdy Solution

STEP 1

Assumptions1. The given sequence is a geometric sequence. The terms of the sequence are $64,16,4,1, \ldots$
3. The common ratio is the same between any two consecutive terms

STEP 2

The common ratio in a geometric sequence is found by dividing any term by the preceding term. We can express this as $r = \frac{a_{n}}{a_{n-1}}$ where $r$ is the common ratio, $a_{n}$ is any term in the sequence, and $a_{n-1}$ is the term preceding $a_{n}$ .

STEP 3

Let's calculate the common ratio using the first two terms of the sequence. $r = \frac{16}{64}$

STEP 4

implify the fraction to find the common ratio.
$r = \frac{16}{64} = \frac{1}{4}$ So, the common ratio for this geometric sequence is $\frac{1}{4}$ .

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