Patterns and Sequences in Mathematics

This video tutorial covers the concept of patterns with constant ratios, explaining how each term in a sequence is obtained by multiplying or dividing by a constant number. It provides examples of both positive and negative constant ratios and demonstrates how to find the next terms and the nth term in a pattern. The tutorial also includes practice problems to reinforce the concepts and encourages viewers to practice further using a provided worksheet.

What does a constant ratio in a pattern mean?

• Each term is squared.

• Each term is subtracted by the same number.

• Each term is multiplied or divided by the same number.

• Each term is added by the same number.

In the sequence 1, 2, 4, 8, what is the constant ratio?

• 4

• 1

• 2

• 3

What indicates a negative constant ratio in a pattern?

• Terms alternate between positive and negative.

• Terms are all zero.

• All terms are negative.

• All terms are positive.

How can division in a pattern be expressed in terms of multiplication?

• By multiplying by the reciprocal of the divisor.

• By adding the divisor.

• By subtracting the divisor.

• By dividing by the reciprocal of the divisor.

What is the rule for the nth term in the sequence -3, -6, -12, -24?

• TN = -3 * 2^n

• TN = -3 * 3^n

• TN = -3 * 3^(n-1)

• TN = -3 * 2^(n-1)

In the sequence 3, 9, 27, 81, what is the constant ratio?

• 2

• 3

• 4

• 5

What is the 9th term in the sequence 3, 9, 27, 81?

• 2,187

• 729

• 6,561

• 19,683

In the sequence 5, 50, 500, 5000, what is the constant ratio?

• 5

• 100

• 10

• 50

What is the 10th term in the sequence 5, 50, 500, 5000?

• 500,000,000

• 50,000,000

• 5,000,000

• 5,000,000,000

In the sequence 5, -10, 20, -40, what is the constant ratio?

• 2

• 3

• -2

• -3