Understanding Quadratic Sequences and Differences

The video tutorial explains how to identify and work with quadratic sequences. It begins by distinguishing between linear and quadratic sequences, highlighting that quadratic sequences have a constant second difference. The tutorial then guides viewers on how to find the next terms in a quadratic sequence by calculating first and second differences. It provides a step-by-step method to determine these differences and use them to predict subsequent terms in the sequence.

What is a characteristic of a linear sequence?

• The sequence is always increasing.

• The terms are all prime numbers.

• The second difference is constant.

• The difference between terms is constant.

What happens to the differences in a non-linear sequence?

• They remain constant.

• They change and are not constant.

• They become zero.

• They form a geometric sequence.

What is the second difference in a sequence?

• The sum of all terms in the sequence.

• The difference of the differences between terms.

• The difference between consecutive terms.

• The difference between the first and last term.

When is a sequence called quadratic?

• When the first difference is constant.

• When the second difference is constant.

• When the sequence forms a perfect square.

• When all terms are even numbers.

What is the purpose of finding the second differences?

• To check if the sequence is geometric.

• To find the sum of the sequence.

• To determine if the sequence is quadratic.

• To identify if the sequence is linear.

What is the constant value of the second difference in the example?

• 4

• 2

• 3

• 5

What is the first step in finding the next terms of a quadratic sequence?

• Calculate the sum of all terms.

• Write down the first differences.

• Multiply all terms by a constant.

• Find the average of the terms.

How do you find the second differences in a sequence?

• By adding all the terms together.

• By finding the differences of the first differences.

• By subtracting the first term from the last.

• By dividing the sequence by a constant.

What should you do after finding the second differences?

• Divide the sequence by the first term.

• Multiply the sequence by two.

• Add arrows for the next terms.

• Subtract the second differences from the terms.

What is the next step after finding the first differences?

• Calculate the second differences.

• Subtract the first differences from the terms.

• Multiply the first differences by two.

• Add the first differences to the sequence.