Question

What is the funtion notation of this sequence?: 2.5,7.5,22.5,67.5,202.5?

Answer 1

Answer:
`f(n)= 2.5(3)^(n-1)`

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) =
`(Second\ term)/(First\ term)=(7.5)/(2.5)=3`

So this sequence follows geometric progression.

nth term in GP =
`ar^(n-1)`

Required function notation:
`f(n)=ar^(n-1)= 2.5(3)^(n-1)`

i.e. the function notation of given sequence :
`f(n)= 2.5(3)^(n-1)`