Partial sums: mixed review

Learning Objectives Identify whether a given series is arithmetic or geometric. Select and apply the correct formula to calculate the partial sum (S_n) of an arithmetic series. Select and apply the correct formula to calculate the partial sum (S_n) of a finite geometric series. Determine the number of terms (n) in a series given its partial sum. Solve multi-step word problems involving partial sums. Interpret and evaluate a series expressed in summation (Sigma) notation. If you get a job offer where you're paid $1 the first day, $2 the second, $4 the third, and so on for a month, should you take it? Let's find out how to calculate your total earnings! 🤑 This tutorial is a mixed review of partial sums. You will learn to quickly identify whether a series is arithme...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific pattern or rule.The list 4, 9, 14, 19, ... is a sequence. SeriesThe sum of the terms in a sequence.The sum 4 + 9 + 14 + 19 + ... is a series. Partial Sum (S_n)The sum of a specified number of terms from the beginning of a sequence. S_n represents the sum of the first 'n' terms.For the sequence 4, 9, 14, 19, ..., the third partial sum is S_3 = 4 + 9 + 14 = 27. Arithmetic SeriesThe sum of the terms of an arithmetic sequence, where a constant value (the common difference, 'd') is added to each term to get the next.2 + 6 + 10 + 14 is an arithmetic series with a common difference d = 4. Geometric SeriesThe sum of the terms of a geometric sequence, where each term is multiplied by...

Partial Sum of an Arithmetic Series S_n = n/2 * (2a_1 + (n-1)d) Use this formula when you know the first term (a_1), the number of terms (n), and the common difference (d). It's the most versatile formula for arithmetic sums. Alternate Partial Sum of an Arithmetic Series S_n = n/2 * (a_1 + a_n) Use this formula when you know the first term (a_1), the last term (a_n), and the number of terms (n). It is a simpler calculation if the last term is known. Partial Sum of a Finite Geometric Series S_n = a_1 * (1 - r^n) / (1 - r), where r ≠ 1 Use this formula for any finite geometric series where you know the first term (a_1), the common ratio (r), and the number of terms (n).