QuestionFind the common ratio of the geometric sequence: $3, 12, 48, 192, \ldots$ A. 9 B. 4 C. 16 D. 3

Studdy Solution

STEP 1

Assumptions1. The sequence given is a geometric sequence. . A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

STEP 2

To find the common ratio of a geometric sequence, we divide any term by its preceding term. Let's denote the common ratio as r.
$r = \frac{Term_{n}}{Term_{n-1}}$

STEP 3

Now, plug in the given values for Term_n (second term which is12) and Term_{n-1} (first term which is3) to calculate the common ratio.
$r = \frac{12}{3}$

STEP 4

Calculate the common ratio.
$r = \frac{12}{3} =4$ The common ratio for this geometric sequence is4. So, the correct answer is B.4.

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