Q1. Consider the lists: 4, 8, 12, 16; 2, 6, 10, 14; 4, 6, 8, 10; 4, 8, 16, 32. Which, if any, identify arithmetic sequences?

Background

Topic: Sequences and Series

This question is testing your ability to recognize arithmetic sequences. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Key Terms and Formulas

• Arithmetic Sequence: A sequence where each term after the first is found by adding a constant difference to the previous term.

• Common Difference (d): The fixed amount added to each term to get the next term.

• General Formula:

• = nth term

• = first term

• = common difference

• = term number

Step-by-Step Guidance

1. For each list, subtract each term from the next to find the difference between consecutive terms.

2. Check if the difference is the same for all consecutive pairs in the list. If it is, the list is an arithmetic sequence.

3. Repeat this process for all four lists provided in the question.

4. Identify which lists have a constant difference and which do not.

Try solving on your own before revealing the answer!