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11X1 T14 05 sum of an arithmetic series (2010)
This document discusses how to calculate the sum of an arithmetic series. It states that if the first term (a), the last term (l), and the common difference (d) between terms are known, then the sum can be calculated as (a + l) * n / 2. If only the number of terms (n) and the common difference are known, then the sum can be calculated as n * (the first term + the last term) / 2. The document then provides an example of terms in an arithmetic series.
11X1 T14 12 applications of ap & gp
The document discusses arithmetic series and provides formulae for calculating terms and sums of arithmetic series. It gives the definition of an arithmetic series as one where the difference between consecutive terms is constant. Formulae are provided for the nth term of an arithmetic series and the sum of the first n terms. An example problem is then given involving calculating the distance swum on the 10th day and the total distance swum in the first 10 days by someone swimming an arithmetic series of distances.
Arithmetic Series
The document summarizes key facts about the mathematician Carl Friedrich Gauss, including his early demonstrations of mathematical genius as a child and his remarkable influence in many fields of mathematics. It then explains Gauss's method for quickly calculating the sum of integers from 1 to 100 by pairing numbers and realizing their sums are all the same. Finally, it presents the general formula for calculating the sum of terms in a finite arithmetic sequence using this pairing method.
Algebra 2 unit 12.2.12.4
The document discusses arithmetic sequences and series. It defines an arithmetic sequence as a sequence where the difference between successive terms is constant. This common difference allows one to determine explicit formulas to calculate any term or the sum of terms. Several examples are provided of finding common differences, explicit formulas for terms, specific terms, and sums of arithmetic series. The key aspects covered are determining if a sequence is arithmetic, finding common differences and explicit rules, using the formulas to calculate terms and sums, and solving word problems involving arithmetic sequences and series.
Number series
El documento presenta diferentes tipos de problemas numéricos, incluyendo series numéricas, analogías numéricas y números fuera de lugar. Algunos ejemplos de series numéricas son aritméticas, geométricas y una combinación de ambas. Los problemas de analogía numérica involucran relaciones como producto de medias igual a producto de extremos. Finalmente, los problemas de números fuera de lugar piden identificar el número que no cumple con una regla dada, como ser primo, cuadrado o criterios de divisibilidad.
11X1 T10 01 definitions & arithmetic series
The document defines an arithmetic series as a sequence of numbers where each term is found by adding a constant amount (called the common difference) to the previous term. The nth term (Tn) of an arithmetic series is equal to the first term (a) plus (n-1) times the common difference (d). An example shows how to find the general term and other properties of a series given two terms. Specifically, if T3=9 and T7=21, the general term is Tn=3n-3 and the first term greater than 500 is T167=501.
11 x1 t14 12 applications of ap & gp (2013)
The document discusses a word problem involving two employees, Anne and Kay, and their annual salaries over multiple years. Anne's starting salary is $50,000 and increases by $2,500 each year. Kay also begins at $50,000 but receives a 4% raise annually. The document sets up the variables to model each salary situation with an arithmetic series for Anne and a geometric series for Kay.
Arithmetic and geometric_sequences
This document discusses arithmetic and geometric sequences and series. It provides examples of finding terms in sequences, determining common differences or ratios, and calculating partial sums and infinite sums. Key concepts covered include using formulas to find the nth term, the sum of the first n terms, and determining whether an infinite series has a sum based on the common ratio. Examples demonstrate applying these concepts to problems involving sales projections, seating in an auditorium, and calculating partial sums of sequences.
Recommended
11X1 T14 05 sum of an arithmetic series (2010)
This document discusses how to calculate the sum of an arithmetic series. It states that if the first term (a), the last term (l), and the common difference (d) between terms are known, then the sum can be calculated as (a + l) * n / 2. If only the number of terms (n) and the common difference are known, then the sum can be calculated as n * (the first term + the last term) / 2. The document then provides an example of terms in an arithmetic series.
11X1 T14 12 applications of ap & gp
The document discusses arithmetic series and provides formulae for calculating terms and sums of arithmetic series. It gives the definition of an arithmetic series as one where the difference between consecutive terms is constant. Formulae are provided for the nth term of an arithmetic series and the sum of the first n terms. An example problem is then given involving calculating the distance swum on the 10th day and the total distance swum in the first 10 days by someone swimming an arithmetic series of distances.
Arithmetic Series
The document summarizes key facts about the mathematician Carl Friedrich Gauss, including his early demonstrations of mathematical genius as a child and his remarkable influence in many fields of mathematics. It then explains Gauss's method for quickly calculating the sum of integers from 1 to 100 by pairing numbers and realizing their sums are all the same. Finally, it presents the general formula for calculating the sum of terms in a finite arithmetic sequence using this pairing method.
Algebra 2 unit 12.2.12.4
The document discusses arithmetic sequences and series. It defines an arithmetic sequence as a sequence where the difference between successive terms is constant. This common difference allows one to determine explicit formulas to calculate any term or the sum of terms. Several examples are provided of finding common differences, explicit formulas for terms, specific terms, and sums of arithmetic series. The key aspects covered are determining if a sequence is arithmetic, finding common differences and explicit rules, using the formulas to calculate terms and sums, and solving word problems involving arithmetic sequences and series.
Number series
El documento presenta diferentes tipos de problemas numéricos, incluyendo series numéricas, analogías numéricas y números fuera de lugar. Algunos ejemplos de series numéricas son aritméticas, geométricas y una combinación de ambas. Los problemas de analogía numérica involucran relaciones como producto de medias igual a producto de extremos. Finalmente, los problemas de números fuera de lugar piden identificar el número que no cumple con una regla dada, como ser primo, cuadrado o criterios de divisibilidad.
11X1 T10 01 definitions & arithmetic series
The document defines an arithmetic series as a sequence of numbers where each term is found by adding a constant amount (called the common difference) to the previous term. The nth term (Tn) of an arithmetic series is equal to the first term (a) plus (n-1) times the common difference (d). An example shows how to find the general term and other properties of a series given two terms. Specifically, if T3=9 and T7=21, the general term is Tn=3n-3 and the first term greater than 500 is T167=501.
11 x1 t14 12 applications of ap & gp (2013)
The document discusses a word problem involving two employees, Anne and Kay, and their annual salaries over multiple years. Anne's starting salary is $50,000 and increases by $2,500 each year. Kay also begins at $50,000 but receives a 4% raise annually. The document sets up the variables to model each salary situation with an arithmetic series for Anne and a geometric series for Kay.
Arithmetic and geometric_sequences
This document discusses arithmetic and geometric sequences and series. It provides examples of finding terms in sequences, determining common differences or ratios, and calculating partial sums and infinite sums. Key concepts covered include using formulas to find the nth term, the sum of the first n terms, and determining whether an infinite series has a sum based on the common ratio. Examples demonstrate applying these concepts to problems involving sales projections, seating in an auditorium, and calculating partial sums of sequences.
ELW/ESL
History is the study and writing down of past human events and scientific discoveries using primary and secondary sources. Primary sources directly from a time period, like documents, art, or objects. Secondary sources interpret and analyze primary sources, and can include textbooks and articles. Historians use these two types of sources to research and write about history for reasons such as money, fame, and preserving the past.
Biologoy Lab Report
1. The document describes a lab experiment that demonstrates natural selection and evolution using colored twinkles ("prey") and student predators.
2. When the lights were turned off in an orange-lit environment, the brown twinkles were least noticeable and were picked least by predators, while green twinkles stood out most and were eliminated first.
3. Over multiple generations, the percentage of brown twinkles increased as they were most adapted to the environment, while colorful twinkles decreased and went extinct, demonstrating natural selection.
Cultural Adventure Plan
The document is a student's plan for a cultural adventure to learn about fruit carving in Thailand. The plan includes: visiting a fruit carving maker to observe and interview them; conducting background research on the history and techniques of fruit carving; and presenting their findings to the class using PowerPoint. The student provides details on the location, date, interview questions, potential language barriers, and how they will document and appreciate their experience.
Rashamon Essay
1) The document discusses the film Rashomon by Akira Kurosawa and the differing viewpoints of critics Errol Morris and Roger Ebert on the concept of truth and reality presented in the film.
2) Morris argues for an absolutist view that there is one objective truth that can be discovered through evidence, while Ebert believes in relativism and that multiple subjective truths exist based on individual perspectives.
3) In Rashomon, different witnesses provide conflicting accounts of a murder, and the document analyzes whose philosophical viewpoint, absolutism or relativism, provides a more convincing interpretation of the film's exploration of truth and human perception.
Senior Seminar Interview Presentation
This document discusses an interview with Dolev Tabacaro about participating in the ISB Idol competition. It forced them to face their fear of performing for an audience for the first time and helped reveal their true self through using both emotion and reason. Emotionally it furthered their desire to perform and helped them overcome their fear, while rationally it involved deductive reasoning, thinking outside the box, and practice to improve their performance skills.
IAT Results - Dolev Tabacaro
The document discusses how one's upbringing and environment can shape their unconscious biases and behaviors. The author argues that growing up in Israel, which has less racial prejudice than America, meant they were not exposed to discrimination against black people. While the media can influence unconscious biases, the author believes taking an implicit association test was inconclusive due to feeling defensive about possibly being prejudiced.
Giacomo dolev
School is the main cause of depression among teens in Italy according to the document. Depression can lead teens to have feelings of hopelessness and consider committing suicide as a solution. The effects of depression include negatively impacting eating and sleeping habits, using drugs and alcohol, and socializing less than before. The causes mentioned are school, trauma, lack of support, and bullying.
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ELW/ESL
History is the study and writing down of past human events and scientific discoveries using primary and secondary sources. Primary sources directly from a time period, like documents, art, or objects. Secondary sources interpret and analyze primary sources, and can include textbooks and articles. Historians use these two types of sources to research and write about history for reasons such as money, fame, and preserving the past.
Biologoy Lab Report
1. The document describes a lab experiment that demonstrates natural selection and evolution using colored twinkles ("prey") and student predators.
2. When the lights were turned off in an orange-lit environment, the brown twinkles were least noticeable and were picked least by predators, while green twinkles stood out most and were eliminated first.
3. Over multiple generations, the percentage of brown twinkles increased as they were most adapted to the environment, while colorful twinkles decreased and went extinct, demonstrating natural selection.
Cultural Adventure Plan
The document is a student's plan for a cultural adventure to learn about fruit carving in Thailand. The plan includes: visiting a fruit carving maker to observe and interview them; conducting background research on the history and techniques of fruit carving; and presenting their findings to the class using PowerPoint. The student provides details on the location, date, interview questions, potential language barriers, and how they will document and appreciate their experience.
Rashamon Essay
1) The document discusses the film Rashomon by Akira Kurosawa and the differing viewpoints of critics Errol Morris and Roger Ebert on the concept of truth and reality presented in the film.
2) Morris argues for an absolutist view that there is one objective truth that can be discovered through evidence, while Ebert believes in relativism and that multiple subjective truths exist based on individual perspectives.
3) In Rashomon, different witnesses provide conflicting accounts of a murder, and the document analyzes whose philosophical viewpoint, absolutism or relativism, provides a more convincing interpretation of the film's exploration of truth and human perception.
Senior Seminar Interview Presentation
This document discusses an interview with Dolev Tabacaro about participating in the ISB Idol competition. It forced them to face their fear of performing for an audience for the first time and helped reveal their true self through using both emotion and reason. Emotionally it furthered their desire to perform and helped them overcome their fear, while rationally it involved deductive reasoning, thinking outside the box, and practice to improve their performance skills.
IAT Results - Dolev Tabacaro
The document discusses how one's upbringing and environment can shape their unconscious biases and behaviors. The author argues that growing up in Israel, which has less racial prejudice than America, meant they were not exposed to discrimination against black people. While the media can influence unconscious biases, the author believes taking an implicit association test was inconclusive due to feeling defensive about possibly being prejudiced.
Giacomo dolev
School is the main cause of depression among teens in Italy according to the document. Depression can lead teens to have feelings of hopelessness and consider committing suicide as a solution. The effects of depression include negatively impacting eating and sleeping habits, using drugs and alcohol, and socializing less than before. The causes mentioned are school, trauma, lack of support, and bullying.