Learning Objectives:

__Math Tutoring on Series__

A **sequence** is an ordered list of terms or elements. For example **a₁, a₂, a₃, ..… aᵣ.** Each term in a sequence is identified by its location in the sequence. So **a₁** is the **first term** in the sequence, **a₂** would be the **second term**; **a₃** would be the **third term** and so on. An **arithmetic sequence **is a sequence that has the pattern of adding the same value to determine consecutive terms. **Summing **or** adding** the terms of an arithmetic sequence creates what is called an **arithmetic series.** So **arithmetic series** of the above sequence is **(a₁ + a₂ + a₃ +…. ..… + aᵣ).** Formulas to find the **r** **th Partial sum** of an arithmetic sequence is,

**Sᵣ = r/2 . (a₁+ aᵣ) or Sᵣ = r/2 . ( 2a₁ + (r-1)d) . **

For a **geometric sequence,** the pattern is that we multiply by a constant to determine consecutive terms. **Summing **or** adding** the terms of a geometric sequence creates what is called a **geometric series.** **Partial sum** of first** r** terms of a geometric series is,

**Sᵣ = a₁(1-Rʳ)/(1-R).**

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**Hook Questions:**

*1. What is the difference between a series and a sequence? *

*2. What is an arithmetic series?*

* **3. What is the formula to find the sum of Geometric series? *

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