Answer:
[tex]a_{n}=1.2 \times(2.5)^{n-1}[/tex]
Step-by-step explanation:
If we observe the given sequence, we find that the ratio of two consecutive terms is the same. i.e.
[tex]\frac{3}{1.2}=2.5\\\\\frac{7.5}{3}=2.5\\\\ \frac{18.75}{7.5}=2.5[/tex]
Such a sequence in which the ratio of consecutive terms remain the same is know as Geometric Sequence. Following formula is used to represent a Geometric Sequence:
[tex]a_{n}=a_{1}\times(r)^{n-1}[/tex]
Here:
[tex]a_{n}[/tex] is the general term. Using the value of n =1,2,3 ... will give us the term of the sequence.
[tex]a_{1}[/tex] is the first term which is 1.2 in this case.
r represents the common ratio which is 2.5.
Using these values we get:
[tex]a_{n}=1.2 \times(2.5)^{n-1}[/tex]
This formula can be used to represent the given sequence.
