MMW 1ST SEM

A ___ is a function from a subset of integer ℤ to a set . We use the notation to denote the image of the integer.

A _________ _______ for the sequence is an equation that expresses an in terms of one or more of the previous terms of the sequence, namely, a0 a1 a2 .... an-1 for all integers n with n > is a nonnegative integer.

Let {an} be a sequence that satisfies the recurrence relation an = an-1 + 3 for n equal 1 with ao = 2. Find the terms a1, a2, a3.

The __________ sequence, f0 f1 f2, … is defined by initial conditions f0 = 0, f1 = 1, and the recurrence relation fn=fn-1+fn-2.

Where n is the number of the term, f0 = 0, and f1 = 1.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

Example 1: What is the 11th Fibonacci Number

The countless presence of the irrational number ϕ (roughly 1.618) in nature paved way for it to be known as the _______________. Also used by several artists to showcase aesthetics and appealing proportions.

________ are never-ending patterns and are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.