Answer:
Option A) [tex]1.2(2.5)^{x-1}[/tex]
Step-by-step explanation:
We are given a series:
[tex]1.2, 3, 7.5, 18.75, ...[/tex]
We know that the given series is a geometric series as
[tex]\displaystyle\frac{3}{1.2} = \frac{7.5}{3} = \frac{18.75}{7.5} = 2.5[/tex]
Geometric Series:
- A geometric series is a series with a constant ratio between successive terms.
- The first term is represented by a
- In the given series a = 1.2
- The common ratio is denoted by r
- For the given series r = 2.5
The [tex]n^{th}[/tex] term of a geometric series is given by:
[tex]a_n = a(r)^{n-1}[/tex]
[tex]a_1= 1.2\\a_2 = 1.2(2.5)^{2-1} = 3\\a_3 = 1.2(2.5)^{3-1} = 7.5\\a_4 = 1.2(2.5)^{4-1} = 18.75[/tex]
Thus, the general term of the given series can be formulated with the help of [tex]f(x) = 1.2(2.5)^{x-1}[/tex]
Option A) [tex]1.2(2.5)^{x-1}[/tex]
