PLEASE HELP ME ASAP!!!!!!!!!!!!!!!!!!!!!!!!! 3) This problem is called the Collatz Conjecture and is an unproven statement in ma

Question

2 years ago

6

PLEASE HELP ME ASAP!!!!!!!!!!!!!!!!!!!!!!!!! 3) This problem is called the Collatz Conjecture and is an unproven statement in ma

thematics. People have used computers to try all the numbers up to 5×260 and many mathematicians believe it to be true, but since all natural numbers are infinite in number, this test does not constitute a proof.
Consider the following pattern generating rule:

If the last number is odd, multiply it by 3 and add 1.

If the last number is even, divide the number by 2.

Repeat.

Show a few different starting numbers and see if you can state what you think always happens. Show at least two different representations.

4) Suppose the Fibonacci sequence started with 2 and 5.

a) List the first 10 terms of the new sequence.

b) Find the sum of the first 10 terms of the new sequence

Mathematics

1 answer:

Aneli [31] · Answer 1 · 2023-03-18T15:17:39+03:00

The set of numbers in the Collatz Conjecture are 1, 4, 2, 1, 4, 2, 1, 4, 2....

<h3>How to generate the numbers in the Collatz Conjecture</h3>

To start with, we make use of the following starting point:

Starting point = 1

The rule is given as:

If the last number is odd, multiply it by 3 and add 1.
If the last number is even, divide the number by 2.

1 is an odd number.

So, we use the first rule

So, we have:

1 * 3 + 1 = 4

4 is an even number.

So, we use the second rule

So, we have:

4/2 = 2

So, the first three numbers in the Collatz Conjecture are:

1, 4, 2

Using the given rules, we have:

1, 4, 2, 1, 4, 2, 1, 4, 2....

The above means that there is only one set of repeating numbers in the Collatz Conjecture.

Hence, the set of numbers in the Collatz Conjecture are 1, 4, 2, 1, 4, 2, 1, 4, 2....

<h3>Fibonacci sequence</h3>

The first and the second numbers are given as:

First = 2

Second = 5

The current term of a Fibonacci sequence is the sum of the previous two terms.

Using the above rule, the first 10 terms are:

2, 5, 7, 12, 19, 31, 50, 81, 131, 212

<h3>The sum of the first 10 terms of the new sequence</h3>

We have:

2, 5, 7, 12, 19, 31, 50, 81, 131, 212

Add the terms

Sum = 2+ 5+ 7+ 12+ 19+31+50+81+131+212

Evaluate

Sum = 550

Hence, the sum of the first 10 terms of the new sequence is 550