Question

5 the sequence below can be described by the equation $a_n = a_1 cdot r^{n - 1}$. find the value of $r$. 3, 12, 48, 192, ... a 4 b 3 c 6 d $\frac{1}{4}$

Explanation:

Step1: Identify the sequence type

The sequence is \(3, 12, 48, 192, \dots\) and the formula given is \(a_n=a_1\cdot r^{n - 1}\), which is the formula for a geometric sequence where \(r\) is the common ratio.

Step2: Calculate the common ratio \(r\)

For a geometric sequence, the common ratio \(r\) is given by \(\frac{a_{n}}{a_{n-1}}\). Let's take the second term \(a_2 = 12\) and the first term \(a_1=3\). Then \(r=\frac{a_2}{a_1}=\frac{12}{3} = 4\). We can verify with other terms, for example, \(\frac{a_3}{a_2}=\frac{48}{12}=4\) and \(\frac{a_4}{a_3}=\frac{192}{48}=4\). So the common ratio \(r = 4\).

Answer:

A. 4