Question

Directions: find the next five terms, then write a conjecture. 1. 13, 18, 23, 28, _______, _______, _______, _______, _______ conjecture: ___________________________________________________________________ ______________________________________________________________________________ 2. 512, 256, 128, 64, _______, _______, _______, _______, _______ conjecture: ___________________________________________________________________ ______________________________________________________________________________ 3. 1, 8, 27, 64, _______, _______, _______, _______, _______ conjecture: ___________________________________________________________________ ______________________________________________________________________________ 4. 2, 3, 5, 7, 11, 13, _______, _______, _______, _______, _______ conjecture: ___________________________________________________________________ ______________________________________________________________________________ 5. i, ii, iii, iv, v, _______, _______, ____

Answer 1

1. 13, 18, 23, 28, 33, 38, 43, 48, 53.  

Conjecture: we add five to the next number 13+5: 18; 18+5: 23.

2. 512, 256, 128, 64, 32, 16, 8, 4, 2  

Conjecture:  Dividing the numbers by 2. 512/2: 256; 256/2:128.

3. 1, 8, 27, 64, 125, 216, 343, 512, 729.  

Conjecture: series of cubic numbers: the base multiplied by 3.  

4. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.  

Conjecture:  prime numbers: are numbers that can only by divided by themselves and by unit

5. i, ii, iii, iv, v, vi, vii, viii, ix, x.

Conjecture: Roman numbers is a numerical system expressed by roman numerals.

Answer 2

Answer:

1. 13, 18, 23, 28, 33, 38, 43, 48, 53 --------> Conjecture: This is a sequence of numbers whose difference from one to another is 5.

2. 512, 256, 128, 64, 32, 16, 8, 4, 2 --------->Conjecture:  This is a sequence of halves of the precedent number starting with 512.

3. 1, 8, 27, 64, 125, 216, 343, 512, 729 ------->Conjecture: This is a sequence of the cubic numbers starting with 1^3 and ending with 9^3.

4. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31--------> Conjecture: This is a sequence of the first prime numbers

5. i, ii, iii, iv, v, vi, vii, viii, ix, x -------> Conjecture: This is a sequence of the roman numbers

Explanation:

1. If you add 5 to each number in the order they appear, you will have as a result the following number in the sequence.

2. If you divide each number by 2 to obtain the half, you will get as a result the following number in the sequence.

3. If you multiply each number 3 times itself, you will find the cube number, that means the number that appears for each value:

1^3= 1 . 1 . 1 = 1

2^3= 2 . 2 . 2 = 8

3^3= 3. 3 . 3 = 27  ..  and so on.

4. The prime numbers are the ones that can be divided just by themselves or by one. They cannot be divided by any other number.

5. This a normal sequence of the roman numbers. It starts in 1 and ends in 10.