Find the sum of a finite arithmetic or geometric series

Learning Objectives Distinguish between an arithmetic and a geometric series. Identify the first term (a₁), common difference (d), common ratio (r), and number of terms (n) for a given series. Apply the correct formula to calculate the sum of a finite arithmetic series. Apply the correct formula to calculate the sum of a finite geometric series. Interpret and evaluate a series expressed in summation (sigma) notation. Solve real-world problems by modeling them as finite arithmetic or geometric series. If you saved $10 this week, $15 next week, and $20 the week after, how much would you have in a year without adding up all 52 numbers one by one? 💰 This tutorial will teach you powerful shortcuts to find the total of a list of numbers, as long as they follow a specific pattern...

TermDefinitionExample SeriesThe sum of the terms in a sequence. A series is represented by adding the terms together.For the sequence 2, 5, 8, 11, the corresponding series is 2 + 5 + 8 + 11. Finite SeriesA series that has a specific, countable number of terms, meaning it has a defined end.The sum of the first 10 positive odd integers: 1 + 3 + 5 + ... + 19. Arithmetic SeriesThe sum of the terms of an arithmetic sequence. In an arithmetic series, the same number (the common difference, 'd') is added to each term to get the next.4 + 9 + 14 + 19 + 24. Here, the common difference 'd' is 5. Geometric SeriesThe sum of the terms of a geometric sequence. In a geometric series, each term is multiplied by the same number (the common ratio, 'r') to get the next.3 + 6 + 1...

Sum of a Finite Arithmetic Series S_n = n/2 * (a_1 + a_n) Use this formula when you know the number of terms (n), the first term (a₁), and the last term (a_n). It's the most direct way to find the sum. Sum of a Finite Arithmetic Series (Alternative) S_n = n/2 * [2a_1 + (n-1)d] Use this formula when you know the number of terms (n), the first term (a₁), and the common difference (d), but not the last term. Sum of a Finite Geometric Series S_n = a_1 * (1 - r^n) / (1 - r) Use this formula for any finite geometric series where the common ratio (r) is not equal to 1. You need the first term (a₁), the common ratio (r), and the number of terms (n).