## Tutoring on Series

Learning Objectives:

#### Understand Arithmetic Series.

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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