Create and extend number patterns using multiples, factors, prime numbers, and specific rules. Explain the…

Question

Create and extend number patterns using multiples, factors, prime numbers, and specific rules. Explain the rules for each pattern.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the number pattern questions:

1. Create a pattern that includes:

a. multiples
- Pattern: $7, 14, 21, 28, 35$
- What is the rule? Each number is a multiple of 7 (or, add 7 to the previous number).
b. factors
- Pattern: The factors of 20 are $1, 2, 4, 5, 10, 20$.
- What is the rule? These are all the numbers that divide 20 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

    $$
    15 \times 2 + 1 = 30 + 1 = 31
    $$

    $$
    31 \times 2 + 1 = 62 + 1 = 63
    $$

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

    $$
    28 \div 2 + 2 = 14 + 2 = 16
    $$

    $$
    16 \div 2 + 2 = 8 + 2 = 10
    $$

Create and extend number patterns using multiples, factors, prime numbers, and specific rules. Explain the rules for each pattern.