Given the recursive definition: a1 = 1, a2 = 4 an = an-2 + n?, n > 2, what is ag? O 120 O None of the choices
Q: Given the recursive definition: a1 = 2, a2 = 6 an = 2an-1 + 3an-2, n> 2, what is a6? O 256 O 162
A: Solution:
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- 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(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 +· · ·+a1Java, 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;}
- 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…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: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 recursive function in Java that accepts an integer as input and returns 1 + 1/2 + 3 + 1/4 + ...(n or 1/n). The answer is the sum of the odd integers from 1 to n plus the sum of the reciprocals of the even integers.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.Consider the recursive procedure which computes the nth Fibonacci number is the one below. procedure Fl (n) //a function which returns the nth Fibonacci number.// if n < 2 then return(n) else return (F2(2,n,1,1)) endif end Fl procedure F2(i,n,x,y) if i
- The type of recursion implemented in the following code is a tail recursion (True or False) ? Please explain/ justify your answer. public class ClassTest { public int test(int val) { if (val <= 0){ return val +1; } else return test(val-1) - test(val-2); } public static void main(String[] args) { ClassTest obj = new ClassTest(); int result = obj.test(4); System.out.println("Output is: " + result); } }Write a program that implements a recursive algorithm that prints the factorial of the first 10 digits (1 to 10 and it is optional if you would like to include 0). The program must use a recursive algorithm and can be implemented in Java.In 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.