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,

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.

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.

explanation:

with the profits from the european sales, merchants purchased europe's manufactured  goods, including tools and weapons. then the merchants shipped those manufactured  goods, along with the  american  sugar and rum, to west africa where they were bartered for  slaves.