Answer :
The exponential function describing the sequence 5, 25, 125, 625, 3125, ... is f(n) = 5^n, where n represents the position of the term in the sequence.
Exponential functions are used to describe a sequence of numbers where each term is multiplied by a common factor to get the next term. In this case, the sequence is 5, 25, 125, 625, 3125, ... To write an exponential function for this sequence, we first identify the common factor between the terms.
Each term is 5 times the previous term, which indicates an exponential relationship with 5 as the base. Now we can write the exponential function as:
f(n) = 5^n
where n is the position of the term in the sequence, starting with n=1 for the first term (5).
For example:
- The 1st term is 5^(1) = 5
- The 2nd term is 5^(2) = 25
- The 3rd term is 5^(3) = 125
- And so on.
This function correctly represents the sequence and can be used to find any term in the sequence.
