### [solution] » 1.A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named

Description

The Question

1.A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named after a French mathematician of the nineteenth century. The first ten terms of the Lucas sequence are 1, 3, 4, 7, 11, 18, 29, 47, 76, 123. What is the eleventh term of the Lucas sequence?

The eleventh term of the Lucas sequence is

2.

The following pattern is established involving terms of the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pattern, and verify it. You may wish to refer to the first few terms of the sequence given in the text.

1=1

1+2=3

1+2=3

1+2+5=8

1+2+5+13=21

1+2+5+13+34=55

Each equation skips the next Fibonacci number to add the one after. Each side of the next equation will equal

Following the pattern, write the next equation.

3. What is the approximate value of the golden ratio to the nearest thousandth?

The approximate value of the golden ratio is

4.What is the exact value of the golden ratio?

5. Find the residue of 227 (mod 14)

#### Solution details

Solution #00070215

##### [solution] » 1.A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named .zip

This paper was answered on 14-Oct-2020

STATUS

QUALITY

Approved

Oct 14, 2020

EXPERT

Tutor

#### BEST TUTORS

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

• As a reference for in-depth understanding of the subject.
• As a source of ideas / reasoning for your own research (if properly referenced)
• For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).
This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.