__Math Tutoring on Sequences__

A **sequence** is an ordered list of terms or elements. For example **a**_{1}, a_{2}, a_{3}, ..… aₓ. Each **term** in a sequence is identified by its location in the **sequence.** So **a**_{1} is the **first term** in the **sequence, a**_{2} would be the **second term; a**_{3} would be the **third term** and so on. There are two types of **sequences**, a **finite sequence, **and** an infinite sequence**. A **finite sequence** is a **sequence** that has a specific number of terms and an** ****infinite sequence** is the one which continues on forever. So the value of** n** is based upon the term that we are looking for in the **sequence.** Another way to express a **sequence** is a **recursive formula, **and this means that each term in a **sequence** is based upon previous terms not the value of **n.** Now let’s talk about two different types of **sequences,** one is an **arithmetic sequence** and the other is a **geometric sequence.** An **arithmetic sequence** is a **sequence** that has the pattern of adding the same value to determine consecutive terms and we say **arithmetic sequences** have a **common difference.** To find the common difference, we can pick any term and subtract the term before it. For a **geometric sequence,** the pattern is that we multiply by a constant to determine consecutive terms. We see **geometric sequences** have a **common ratio** other than a common difference. We can calculate that by taking any term in the **sequence** and dividing by the term before it.

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**Hook Questions:**

*1. **What is an ***Arithmetic sequence?**

*2. **Define ***Geometric sequence.**

*3. **What is the ***Recursive formula?**

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Struggling with **Sequences? **Need math help for homework? You are not the only one. Fortunately, our experts in math tutoring** **are online now and are ready to help.