Create and extend number patterns involving multiples, factors, prime numbers, and specific arithmetic rules.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the number pattern questions:

1. Create a pattern that includes:

a. multiples
- Pattern: $6, 12, 18, 24, 30$
- What is the rule? Each number is a multiple of 6 (or, add 6 to the previous number).
b. factors
- Pattern: The factors of 36 are $1, 2, 3, 4, 6, 9, 12, 18, 36$.
- What is the rule? These are all the numbers that divide 36 exactly.

2. Extend the following pattern.

a. Tip: prime numbers are special numbers that can only be divided by themselves and 1. 2, 3, 5, 7, 11, 13, 17, 19
- The next prime numbers after 11 are 13, 17, and 19.
b. Rule: multiply by 2 and add 1. 1, 3, 7, 15, 31, 63, 127

For the term after 15
$15 \times 2 + 1 = 30 + 1 = 31$ .
For the term after 31
$31 \times 2 + 1 = 62 + 1 = 63$ .
For the term after 63
$63 \times 2 + 1 = 126 + 1 = 127$ .
- c. Rule: divide by 2 and add 2. 100, 52, 28, 16, 10, 7
For the term after 28
$28 \div 2 + 2 = 14 + 2 = 16$ .
For the term after 16
$16 \div 2 + 2 = 8 + 2 = 10$ .
For the term after 10
$10 \div 2 + 2 = 5 + 2 = 7$ .

3. Create two of your own number patterns and ask your friend to extend it.
- a.
  
  Pattern: $10, 20, 30, 40, 50, \dots$
  
  Rule: Add 10 to the previous number.
- b.
  
  Pattern: $3, 9, 27, 81, 243, \dots$
  
  Rule: Multiply the previous number by 3.

Step-by-step solution