Question

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

Answer 1

Answer: $f(n)= 2.5(3)^{n-1}$

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) = $\dfrac{Second\ term}{First\ term}=\dfrac{7.5}{2.5}=3$

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 :  $f(n)= 2.5(3)^{n-1}$