Write down a recurrence relation and the closed form for

Question

Problem

For this problem, you are asked to write down a **recurrence relation** and the **closed form** for each of the sequences described below. In each case the indices n are natural numbers and thus n  0.

1. a_n = 1, 2, 4, 8, 16, : : : (the sequence of all powers of 2).

2. b_n = 1, 3, 2, 9, 4, 27, 8, 81, : : : (altenating powers of 2 and 3).

3. c_n = 0, 1, 3, 6, 10, 15, : : : (Hint: look at the dierences between successive elements. That should immediately suggest a recurrence. )

4. d_n = 1, 0, 1, 0, 1, 0, 1, 0, : : : (sequence of alternating 1s and 0s).

5. e_n = 1, 1, 0, 0, 1, 1, 0, 0, : : : ( block of two ones, followed by a block of two zeros, followed by a block of two ones ...)

Attachment:- Assignment1.pdf