A recursive function is a function that calls itself until it reaches a base case, which is a condition that stops the function from calling itself again. This allows the function to solve complex problems by breaking them down into smaller and simpler subproblems.
The formula for this recursive function is An+1 = (8/9)An, where An represents the value of the function at the nth term and An+1 represents the value at the (n+1)th term.
To solve a recursive function, you need to first identify the base case, which is the condition that will stop the function from calling itself again. Then, you can use the formula to calculate the value of the function at each term until you reach the base case. Finally, you can substitute the values back into the formula to get the solution.
The initial value for the recursive function A0 is usually given in the problem or can be determined by the base case. In some cases, it may be assumed to be 1 or 0, but it is important to check with the problem statement to determine the actual initial value.
Recursive functions have many practical applications in computer science, mathematics, and other fields. Some examples include calculating the factorial of a number, finding the nth term in a sequence, and traversing data structures such as trees and graphs. They are also used in algorithms for sorting, searching, and other problem-solving techniques.