Write a recursive function code that finds the elements of the given sequence: a = 3a.+ n², and a 1. What is the time complexity of your code? Explain it.
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- Write a recursive implementation of Euclid's Algorith for finding the greatest common divisor(GCD) of two intergers. Descriptions of this algorithm are available in algebra books and on theweb. (Note: A nonrecursive version of the GCD problem was given in the programming exercisesfor Chapter 7.) Write a test program that calls your GCD procedure five times, using thefollowing pairs of integers: (5,20),(24,18),(11,7),(432,226),(26,13). After each procedure call,display the GCD.Consider a recursive function, called f, that computes powers of 3 using only the + operator. Assume n > = 0. int f(int n) { if (n == 0) return 1; return f(n-1) + f(n-1) + f(n-1); } Give an optimized version of f, called g, where we save the result of the recursive call to a temporary variable t, then return t+t+t. i got int g(int n) { if (n == 0) return 1; int t = g(n - 1); return t+t+t; } so now Write a recurrence relation for T(n), the number addition operations performed by g(n) in terms of n.SML programming Write a recursive function np(n) which takes a non negative n and generates a list of numbers from n+1 down to 0. You may assume that input of n is always valid. Must use identical function name and parameter(s). np(4)⟶[5,4,3,2,1,0]
- Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.Write a recursive Python function named pgcd, to find and return the Greatest Common Divisor (GCD) of two numbers x and y passed in parameters. • Test it gcd (1234,4321) gcd (8192,192)In kotlin, Write a recursive function with an expression body that takes a list of Pairs in which each value may be of any type, and returns a list of the first elements from each pair.
- Suppose a recursive function f(n+1)=f(n)+3 and f(3)=10. What is the value of f(5)•rewrite calculateSum function as a recursive function. m(i) = m(i-1) + i/(i+1), where i >=1In program C Write a recursive function find_sum(n)that calculates the sum of successive integers starting at 1and ending at n(i. e., find_sum( n) = 1 + 2 . . .+( n -1) + n.