Solving problems involving sequences, such as finding sums, averages, or positions.īy utilizing our platform, students benefit from:.Analyzing arithmetic sequences and geometric sequences.Finding terms of a sequence, including the nth term.Generating sequences using explicit and recursive formulas.Identifying patterns and properties of sequences.Students can develop the following skills and knowledge through our resources: By becoming a member of our platform, users gain access to a variety of materials designed to enhance their understanding and proficiency in working with sequences. Our website offers a comprehensive collection of resources and worksheets dedicated to general sequences. Suppose everyday money was deposited into an account for you.Sequences and Series General Sequences Worksheets To find the general formula for a geometric sequence: Find the general rule for the following:ġ8 Geometric Series To find the sum of a finite geometric series, use the following formula: Evaluate the following: You will multiply by a common ratio to find the next term. Can you find the ratio from the sequence in the previous slide? Find the ratio for the following sequence:ġ7 Geometric Sequences A geometric sequence is kind of like exponential growth or decay. To find r we simply divide any term by its previous term. OMG, how do you find the ratio here?ġ6 Geometric Sequences Geometric Sequences have a common ratio. How do you find the ratios? Sometimes you can just look. How much money does the concert hall take in for a sold out event?ġ4 Geometric Sequences With arithmetic sequences we added something each time With geometric sequences we multiply by something each timeġ5 Geometric Sequences Here are some geometric sequences: Suppose each seat in rows 1 through 11 of the concert hall costs $24, each seat in rows 12 through 22 costs $18 and each seat in rows 23 through 32 costs $12. How much would it cost for the company to drill a 100-foot well?ġ3 Application #2 The first row of a concert hall has 25 seats, and each row after that has one more seat than the row before it. This means that it would cost $45.75 for the company to drill 3 feet. We did this on our first example which came out to be : an= 3n – 1 Now you plug in 20 for n: a20 = 3(20)-1=60-1=59 Now use to find the sum of first 20 terms That is your answerġ2 Application #1 A well-drilling company charges $15 for drilling the first foot, $15.25 for the second foot, $15.50 for the third foot, and so on. First off, you have to find a formula for the nth term. The equation for the sum of a finite arithmetic series is:ġ1 Find the Sum of a Finite Arithmetic Series (cont.)Įxample: … Find the sum of the first 20 terms. The expression formed by adding the terms of an arithmetic sequence is called an arithmetic series. Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050.ġ0 Find the Sum of a Finite Arithmetic Series The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Büttner, tried to occupy pupils by making them add a list of integers in arithmetic progression as the story is most often told, these were the numbers from 1 to 100. Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Īnother famous story has it that in primary school his teacher, J.G. The nth term of an arithmetic sequence with first term a1 and common difference “d” is:Įxample: 2, 5, 8, 11, 14, … The common difference is 3 Use the equation : an= a1 + (n – 1)d a1= 2 an= 2 + (n – 1)3 an= 2 + 3n – 3 an= 3n – 1 That is your rule for the nth term What is the difference? What is arithmetic, what is geometric? What is sigma (summation) notation? What formulas are important?Īn arithmetic sequence is when there is a common difference between consecutive terms. + 9 + 10Ĥ Sequences and Series What is a sequence? What is a series? 2 Vocabulary Sequence Series Term Domain Range Infinite Finiteģ Sequences and Series Find the sum 1 + 2 + 3 +.
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