Given the recursive definition: a1 = 2, a2 = 6 an = 2an-1 + 3an-2, n> 2, what is a6? O 256 O 162
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A: Given: Write a recursive mathematical definition for computing 2n for a positive integer n.
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- (a) Give a recursive definition of F(n) where F(n) =1+2+3+....+n. (b) Find the value of a4 if a1 = 1, a2 = 2, and an =an−1 + an−2 +· · ·+a1In Java - Implementing Recursion to Provide a Product Using recursion, create a program that will allow a user to enter five numbers. The program will provide the product of all five numbers using recursive methods.Which is the base case of the following recursion function: def mult3(n): if n == 1: return 3 else: return mult3(n-1) + 3 else n == 1 mult3(n) return mult3(n-1) + 3
- hi,it is wrong agai n fib(n) 2 1 2 1 2 1 2 1 2 1Number of recursive calls: 5 but have to:In Java, recursion can be used to solve different problems such as factorial of a given number. ___________________ implies 5 x 4 x 3 x 2 x 1.Which recursive sequence would produce the sequence 6,−9,21,...6,−9,21,...?
- Java, Demonstrate how factorial(4) is computed given the following recursive method for factorial:public int factorial(int n){if (n > 1) return factorial(n - 1) * n;else return 1;}Implement a recursive program that takes in a number and finds the square of that number through addition. For example if the number 3 is entered, you would add 3+3+3=9. If 4 is entered you would add 4+4+4+4=16. This program must be implemented using recursion to add the numbers together. I need the MIPS Code for the above.The following recursion occurs when there are more than two calls for each non-base case: : c)Multiple recursion d)Two Step Recursion a)Linear recursion b)Binary recursion Simple answer. Choose a or b or c or d.
- 2._____'ccccc6 sloc) 497 Bytes Write a recursive function that returns the sum of the digits of a given integer.Input format :Integer NOutput format :Sum of digits of NConstraints :0 <= N <= 10^9Sample Input 1 :12345Sample Output 1 :15Sample Input 2 :9Sample Output 2 :9 Solution:///////////// public class solution { public static int sumOfDigits(int input){ int sum; if(input<10){ return input; } sum = (input % 10) + sumOfDigits(input / 10); return sum; }}..Question#1: Let P and Q be integers and suppose F (P, Q) is recursively defined by: F(int P, int Q) if (P == 0) return Q else return F(P- 1, P + Q) Find and Trace F(8,1)Write a program that performs the following functionalities:1. Fibonacci: a recursive function that computes the fibonacci series, which is defined as followsfibonacci (n) = fibonacci(n-2) + fibonacci(n-1)fibonacci(0) = 0fibonacci(1) = 1 So the fibonacci looks like: 0 1 1 2 3 5 8 13 21 34 …. Therefore, fibonacci(4) = 3, fibonacci(5) = 5, fibonacci(7)=13 2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1) 3. Largest: a recursive function that computes the largest value for an integer array of positiveand negative values. For example, for the array below, the function largest should return 22,which is the largest value in the array. You can assume there are no more 20 integers in thearray. Think of how to formulate the recurrence relation in this problem yourself. 4. The 4th problem mimics the situation where eagles flying in the sky can be spotted and…