use the rule to write the first twelve numbers in the pattern. describe another pattern in the numbers.
Rule: Add 3, subtract 2 First term: 7
The simpler rule is : add 1
so the terms are:
7, 8, 9, ...
To write the first twelve numbers in the given pattern, we will start with the first term, which is 7, and apply the rule "Add 3, subtract 2" repeatedly:
Term 1: 7
Term 2: (7 + 3) - 2 = 8
Term 3: (8 + 3) - 2 = 9
Term 4: (9 + 3) - 2 = 10
Term 5: (10 + 3) - 2 = 11
Term 6: (11 + 3) - 2 = 12
Term 7: (12 + 3) - 2 = 13
Term 8: (13 + 3) - 2 = 14
Term 9: (14 + 3) - 2 = 15
Term 10: (15 + 3) - 2 = 16
Term 11: (16 + 3) - 2 = 17
Term 12: (17 + 3) - 2 = 18
Now that we have the first twelve numbers in this pattern, let's describe another pattern that can be observed in these numbers. One pattern is that the numbers are consecutive integers, starting from 7 and increasing by 1 each time.
To generate the first twelve numbers in the pattern using the given rule (add 3, subtract 2), you can start with the first term, which is 7, and then apply the rule successively to obtain the subsequent terms. Here's how it would look:
First term: 7
Second term: 7 + 3 = 10
Third term: 10 - 2 = 8
Fourth term: 8 + 3 = 11
Fifth term: 11 - 2 = 9
Sixth term: 9 + 3 = 12
Seventh term: 12 - 2 = 10
Eighth term: 10 + 3 = 13
Ninth term: 13 - 2 = 11
Tenth term: 11 + 3 = 14
Eleventh term: 14 - 2 = 12
Twelfth term: 12 + 3 = 15
The first twelve numbers in the pattern are: 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15.
Now, let's describe another pattern in these numbers. One potential pattern that emerges is an alternating sequence of even and odd numbers. Notice that the second term (10) and fourth term (11) are odd, while the third term (8) and fifth term (9) are even. This alternating pattern continues throughout the sequence.