Create and extend number patterns based on rules like multiples, factors, prime numbers, and arithmetic…

Question

Create and extend number patterns based on rules like multiples, factors, prime numbers, and arithmetic operations.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the number pattern questions:

1. Create a pattern that includes:

a. multiples
- Pattern: $5, 10, 15, 20, 25$
- What is the rule? Each number is a multiple of 5 (or, add 5 to the previous number).
b. factors
- Pattern: The factors of 15 are $1, 3, 5, 15$.
- What is the rule? These are all the numbers that divide 15 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 based on rules like multiples, factors, prime numbers, and arithmetic operations.