A) Recurrence Relations

1) {5, 9, 13, } is an Arithmetic Sequence. Write the recursive formula for a_n+1

2) {3, 6, 12,} is a Geometric Sequence. Write the recursive formula for a_n+1

3) For each of the next two examples, write a RECURSIVE PYTHON program. Pass the designated value for n to your program and run the program. Submit a screen shot of the code in the IDLE window and of your output.

i.) The recursive function that will print all the integers between n and 1 in descending order. Pass the value n = 4 to the function.

ii.) The recursive function that will print the value of x raised to a power n. Pass your function the values x = 4 and n = 3 and print the OUTPUT. Also, manually TRACE what happens at each recursive step of the program.

B) Prove using the Principle of Mathematical Induction (PMI)

1.) 2n>= n + 1, for all n >= 1

2.) 3ⁿ 1 is divisible by 2 for all n >=1

3.) 6 + 12 +18 ++6n = 3n (n+1) for all n >=1