Answer: [tex]f(n)= 2.5(3)^{n-1}[/tex]
Step-by-step explanation:
The given sequence : 2.5,7.5,22.5,67.5,202.5
here first term (a)= 2.5
Second term = 7.5
Third term = 22.5 and so on
The difference between the two consecutive terms is increasing but have common ratio as:
Common ratio (r) = [tex]\dfrac{Second\ term}{First\ term}=\dfrac{7.5}{2.5}=3[/tex]
So this sequence follows geometric progression.
nth term in GP = [tex]ar^{n-1}[/tex]
Required function notation: [tex]f(n)=ar^{n-1}= 2.5(3)^{n-1}[/tex]
i.e. the function notation of given sequence : [tex]f(n)= 2.5(3)^{n-1}[/tex]
