Find the sum of a finite arithmetic or geometric series

Learning Objectives Differentiate between an arithmetic and a geometric series by analyzing its terms. Identify the first term (a₁), common difference (d), common ratio (r), and number of terms (n) in a finite series. Apply the correct formula to calculate the sum of a finite arithmetic series (Sₙ). Apply the correct formula to calculate the sum of a finite geometric series (Sₙ). Interpret and evaluate a finite series expressed in summation (sigma) notation. Model and solve real-world problems involving finite series, such as loan amortization or structured savings plans. If you saved $1 on day one, $2 on day two, $4 on day three, and so on, how much money would you have after just one month? 🤯 The answer might surprise you! This tutorial provides the essential tools to fi...

TermDefinitionExample SeriesThe sum of the terms in a sequence. A series is finite if it has a specific number of terms.For the sequence 2, 5, 8, 11, the corresponding finite series is 2 + 5 + 8 + 11. Arithmetic SeriesA series in which the difference between any two consecutive terms is a constant value, known as the common difference (d).The series 5 + 10 + 15 + 20 + 25 is an arithmetic series with a common difference of 5. Geometric SeriesA series in which the ratio between any two consecutive terms is a constant value, known as the common ratio (r).The series 3 + 6 + 12 + 24 + 48 is a geometric series with a common ratio of 2. Common Difference (d)The constant value that is added to each term to get the next term in an arithmetic series. It can be positive, negative, or zero.In the ser...

Sum of a Finite Arithmetic Series S_n = \frac{n}{2}(a_1 + a_n) OR S_n = \frac{n}{2}(2a_1 + (n-1)d) Use this to find the sum (Sₙ) of the first 'n' terms. The first version is efficient if you know the first (a₁) and last (aₙ) terms. The second is used when you know the first term, the number of terms (n), and the common difference (d). Sum of a Finite Geometric Series S_n = a_1 \frac{1 - r^n}{1 - r}, \text{ where } r \neq 1 Use this to find the sum (Sₙ) of the first 'n' terms of a geometric series. You need the first term (a₁), the common ratio (r), and the number of terms (n).