Arithmetic and geometric sequences and series

    • [DOC File]An Investigation of Sequences and Series

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      As expected, finite arithmetic and finite geometric series turn out to be nice and easily predictable. Part 3: Let’s re-visit our first two arithmetic sequences. a: Use the rule you discovered in Part 1a and your calculator’s seq( and cumsum( functions to store the following sequence to List1, List2, and List3.

    • [DOC File]Department of Mathematics: Home : The University of Akron

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      Partial sums, convergent, divergent, infinite series, geometric series, sum of a convergent infinite geometric series. NCTM Standards Addressed: Standards: Patterns, Functions, and Algebra Grade 12, Indicators 1 & 2 and Grade 8, Indicator 2 . 12:1 -- “Analyze the behavior of arithmetic and geometric sequences and series as the number

    • [DOC File]CHAPTER 7: SEQUENCES, SERIES, AND COMBINATORICS

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      ARITHMETIC SEQUENCES AND SERIES. Arithmetic Sequences: A sequence is . arithmetic. if there exists a number d, called the . common difference, such that for any integer . nth Term of an Arithmetic Sequence: The . nth term . of an arithmetic sequence is given by for any integer . Example: Find the 14th term of the arithmetic sequence 4, 7, 10 ...

    • [DOCX File]Mathematics Instructional Plan - Algebra II

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      Arithmetic and Geometric Sequencesand Series. Strand: Functions. Topic: Exploring sequences and series. Primary SOL: AII.5The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first . n. terms, finding the . n.

    • [DOC File]Arithmetic Sequences

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      Arithmetic Sequences. Definition: An arithmetic sequence is a sequence in which each term, after the first, is the sum of the preceding term and a common difference. An arithmetic sequence can be represented by a1, a1 +d, a1 + 2d, …. In the sequence 2, 5, 8, ….. the common difference is 3.

    • [DOC File]WORKSHEET: Arithmetic Sequence & Series Word Problems

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      ARITHMETIC SEQUENCES & SERIES WORKSHEET. The . general term of an arithmetic sequence. is given by the formula . an = a1 + (n - 1)d. where . a1. is the . first term. in the sequence and . d. is the . common difference. Finding the sum of a given arithmetic sequence: 1. Identify a1, n, and d for the sequence. 2. Find an using an = a1 + (n - 1)d ...

    • [DOC File]Arithmetic Sequence

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      Arithmetic Series. Geometric Sequences. Explicit formula . Recursive formula Geometric Series. Arithmetic mean. Ex.1) Find arithmetic mean of 5 and 10. 7.5 Ex. 2) the 2 arithmetic mean of 6 and 12. 8, 10. Ex 3) the 3 arithmetic mean of 8 and 16. 10, 12, 14. Etc… Geometric mean. Ex. 1) Find geometric mean of 2 and 18. 6 Ex. 2) the 2 geometric ...

    • [DOC File]Lesson Title

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      Reporting Category Expressions and Operations. Topic. Exploring sequences and series. Primary SOL AII.2 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas.

    • [DOC File]Story Board Assignment for

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      In our studies of Sequences and Series, we discussed many topics about arithmetic and geometric sequences and series. You have seen how to find the nth term, write the general term formula and find the sum of each type of series. You learned that a geometric series can be finite or infinite and depending on the common ratio, the series might ...

    • [DOC File]Arithmetic Sequences

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      Arithmetic Sequences. Definition: An arithmetic sequence is a sequence in which each term, after the first, is the sum of the preceding term and a common difference. An arithmetic sequence can be represented by a1, a1 +d, a1 + 2d, …. In the sequence 2, 5, 8, ….. the common difference is 3.

    • Mathematics Advanced Year 12 Sample Unit Financial Mathematics

      The teacher introduces the notion of classifying sequences and series according to their generating pattern. Specifically, sequences and series that are generated through additive processes are classified as arithmetic and those generated through multiplicative processes are classified as geometric.. With teacher assistance as necessary, the class explores a variety of arithmetic sequences and ...

    • [DOC File]Arithmetic and Geometric Sequences

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      Arithmetic and Geometric Sequences. A sequence is a list of numbers or objects, called terms, in a certain order. In an . arithmetic sequence, the difference between one term and the next is always the same. This difference is called a . common difference. The common difference is added to each term to get the next term. 2, 5, 8, 11, 14, …

    • [DOC File]Level 2 Mathematics and Statistics internal assessment ...

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      Examples of situations that involve arithmetic sequences and series are: table mortgages, mathematical patterns, patterns in nature, tiling patterns, and hire purchase payments. Examples of situations that involve geometric sequences and series are: loan repayments, population predictions, car depreciation, half-life of radioactive material ...

    • [DOC File]ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM EXAMPLES

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      ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM EXAMPLES. A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks.

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