# **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. --- --- # **Key Concepts** This exercise focuses on the following concepts: * **Arithmetic Sequence:** A sequence of numbers where the difference between consecutive terms is constant. This constant difference is known as the common difference (*d*). * **General Term of an Arithmetic Sequence:** Any term in an arithmetic sequence can be found if the first term (*a₁*) and the common difference (*d*) are known. * **Arithmetic Mean:** The average of a set of numbers, which in the context of an arithmetic sequence, is a term or terms between any two non-consecutive terms. --- # **Important Formulas** Below are the key formulas used in this exercise: | Formula | Description | | :--- | :--- | | **General Term of an Arithmetic Sequence** | The formula to find the nth term of an arithmetic sequence. | | $a_n = a_1 + (n-1)d$ | Where *aₙ* is the nth term, *a₁* is the first term, *n* is the term number, and *d* is the common difference. | | **Common Difference** | The formula to find the common difference between terms. | | $d = a_n - a_{n-1}$ | Where *d* is the common difference, *aₙ* is the current term, and *aₙ₋₁* is the previous term. | | **Arithmetic Mean** | The formula to find the arithmetic mean (A) between two numbers *a* and *c*. | | $A = \frac{a+c}{2}$ | Where *A* is the arithmetic mean. | --- # **Summary** This exercise provides a comprehensive review of arithmetic sequences. The questions cover fundamental skills such as determining the terms of a sequence given the first term and common difference, and finding the common difference from a given sequence. It progresses to more advanced problems like finding missing terms and the first term when two other terms are known. The exercise also includes practical word problems that require the application of arithmetic sequence formulas to real-world scenarios. A significant portion of the questions is dedicated to understanding and calculating the arithmetic mean between two numbers, including finding multiple arithmetic means. Mastering these questions will build a strong foundation in the properties and applications of arithmetic sequences. --- # **Reference Videos** Below are recommended video explanations for this exercise: