Question

mathematics i a-g cr sem a aguirre
exponential functions
which formula can be used to describe the sequence?
1.2, 3, 7.5, 18.75,...
$f(x) = 1.2(2.5)^x$
$f(x) = 2.5(1.2)^{x - 1}$
$f(x) = 1.2(2.5)^{x - 1}$
$f(x) = 2.5(1.2)^x$
test
mark and return
13 of 25

Explanation:

Step1: Identify the type of sequence

The sequence \(1.2, 3, 7.5, 18.75, \dots\) is a geometric sequence because each term is multiplied by a common ratio. Let's find the common ratio \(r\) by dividing a term by its previous term. For example, \(\frac{3}{1.2} = 2.5\), \(\frac{7.5}{3}=2.5\), \(\frac{18.75}{7.5} = 2.5\). So the common ratio \(r = 2.5\).

Step2: Recall the formula for a geometric sequence

The general formula for a geometric sequence is \(f(x)=a_1(r)^{x - 1}\), where \(a_1\) is the first term and \(r\) is the common ratio. Here, the first term \(a_1=1.2\) and \(r = 2.5\).

Step3: Substitute the values into the formula

Substituting \(a_1 = 1.2\) and \(r=2.5\) into the formula \(f(x)=a_1(r)^{x - 1}\), we get \(f(x)=1.2(2.5)^{x - 1}\).

Answer:

\(f(x) = 1.2(2.5)^{x - 1}\) (the third option in the list of given formulas)