Lesson 1 sequence and series
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This document discusses sequences and series in mathematics. It begins with an introduction to sequences as ordered lists that follow a pattern or rule. Examples of different types of sequences are given, such as finite vs infinite sequences. Patterns in example sequences are identified. The document then discusses generating patterns in sequences and finding the next terms. Series are introduced as the sum of all terms in a sequence. Examples are given of finding the series of sequences. Students are directed to practice examples in their book and check Canvas for an asynchronous assignment.
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Arithmetic sequence
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. The formula for the nth term of an arithmetic sequence is an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. This document provides examples of using the arithmetic sequence formula to find terms, common differences, and formulas for arithmetic sequences given various terms or conditions.
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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.
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This document provides instruction on finding the sum of finite geometric sequences. It defines a geometric series as the sum of terms in a geometric sequence. It gives examples of finding the sum of the first n terms when the ratio r is -1, 1, or another value. The key formula provided is Sn = a1rn-1/(r-1) for finding the sum of a finite geometric sequence, where a1 is the first term, r is the common ratio, and n is the number of terms. An example problem applies this to find the total distance traveled by a ball bouncing repeatedly to 40% of its previous height.
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Geometric Sequence
The document discusses geometric sequences and series. It defines a geometric sequence as a sequence where each term is obtained by multiplying the preceding term by a constant called the common ratio. It provides examples and discusses how to find the nth term, determine if a sequence is geometric, and calculate the geometric mean. It then introduces geometric series as the sum of the first n terms of a geometric sequence and provides the formulas to calculate finite and infinite geometric series.
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This document discusses geometric sequences and provides examples. It defines a geometric sequence as a sequence where each term is found by multiplying or dividing the same value from one term to the next. An example given is 2, 4, 8, 16, 32, 64, 128, etc. The document also provides the general formula for a geometric sequence as {a, ar, ar2, ar3, ...} where a is the first term and r is the common ratio between terms. It gives practice problems for finding missing terms and the common ratio of geometric sequences.
Arithmetic sequence
This document discusses arithmetic sequences and provides formulas for writing recursive and explicit expressions for terms in an arithmetic sequence. It gives an example of the arithmetic sequence 20, 24, 28, 32, 36, which has a common difference of 4. The recursive formula is defined as an = an-1 + d. The explicit or closed form formula is defined as an = a1 + (n-1)d, which allows finding any term without knowing all previous terms. It asks the reader to find the term number for the last term in the sequence -6, -3, 0, 3, ..., 147 and to determine the values of d and c in the explicit formula an = dn + c for the sequence 8, 6,
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This document provides instruction on finding the sum of finite geometric sequences. It defines a geometric series as the sum of terms in a geometric sequence. It gives examples of finding the sum of the first n terms when the ratio r is -1, 1, or another value. The key formula provided is Sn = a1rn-1/(r-1) for finding the sum of a finite geometric sequence, where a1 is the first term, r is the common ratio, and n is the number of terms. An example problem applies this to find the total distance traveled by a ball bouncing repeatedly to 40% of its previous height.
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This document discusses geometric sequences and provides examples. It defines a geometric sequence as a sequence where each term is found by multiplying or dividing the same value from one term to the next. An example given is 2, 4, 8, 16, 32, 64, 128, etc. The document also provides the general formula for a geometric sequence as {a, ar, ar2, ar3, ...} where a is the first term and r is the common ratio between terms. It gives practice problems for finding missing terms and the common ratio of geometric sequences.
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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This document discusses arithmetic and geometric sequences. An arithmetic sequence is one where the difference between consecutive terms is constant, while a geometric sequence is one where the ratio between consecutive terms is constant. Formulas are provided to calculate individual terms and the sum of terms for both arithmetic and geometric sequences. Examples are worked through demonstrating how to identify sequences and apply the formulas to problems involving cash prizes, savings accounts, and other real-world scenarios.
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This document defines and provides examples of arithmetic sequences. An arithmetic sequence is a sequence where each term after the first is obtained by adding a constant value, called the common difference, to the preceding term. The document provides the arithmetic sequence formula and examples of using it to find terms and sums of arithmetic sequences. Various activities are presented for students to practice identifying, describing, and working with arithmetic sequences.
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2. It starts with a square of area 64 square units and folds the corners into the center, halving the side length and quartering the area each time.
3. The reader is to repeat this folding process three times and record the resulting areas in a provided table.
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The document discusses sequences and series. It defines what a sequence is, including the general term and different types of sequences such as arithmetic, finite, infinite, monotone, and piecewise sequences. It also defines arithmetic sequences specifically and provides the general term for an arithmetic sequence as an = a1 + (n - 1)d, where d is the common difference. Examples are given throughout to illustrate sequence concepts and properties.
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For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
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https://tinyurl.com/ycjp8r7u
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document describes an abstract reasoning test. It includes examples of sequences with patterns of increasing or decreasing numbers. It explains that abstract reasoning tests often involve identifying the pattern or rule governing a sequence and determining the next terms. It provides examples of arithmetic sequences where each term is calculated by adding or subtracting a constant from the previous term. It also gives examples of sequences that are and are not arithmetic sequences. The document aims to define arithmetic sequences, illustrate them, and explain how to determine the nth term, number of terms, and common difference of an arithmetic sequence.
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The document defines sequences and series. It explains that a sequence is an ordered list of numbers with a specific pattern, while a series is the sum of the terms in a sequence. The document provides examples of arithmetic and geometric sequences, and explains how to determine the nth term of each using formulas involving the first term, common difference or ratio, and position of the term. It also discusses finite vs infinite sequences and gives examples of sequences in real world contexts like running training and loan interest.
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Lesson 1 sequence and series
- 2. Can you share to the class the daily routine you are doing as you wake up in the morning
- 3. How about, can you tell step by step how do you your favorite me the process prepare food?
- 4. What do you think will happen next?
- 5. What comes next? 1, 4, 9 16, ...
- 6. What comes next? J, F, M, A, M, J,...
- 7. What comes next? 1, 3, 6, 10, 15, ...
- 9. Sequence A list of numbers or objects in a special order. ordered set of mathematical quantities called terms an arrangement of any objects or a set of numbers in a particular order followed by some rule
- 11. Spot the Difference Sequence A 2, 4, 6, 8, 10, 12, 14, 16 Sequence B 2, 4, 6, 8, 10, 12, 14, 16, ...
- 12. Types of Sequence Sequence A is a Finite Sequence becauseit has a last term Sequence B is an Infinite Sequence because of the three dots that signifies no end
- 13. Let's Generate Patterns Example 1: 2, 5, 8, 11, 14 Example 2 7, 9, 11, 13, 15, 17
- 14. Find the next terms Example 1: 3n + 1 , 4, 7, 10, .... 6n , Example 2 6, 12, 18, 24, ....
- 15. Let's Apply You own a fruit stand, To make your display more attractive, you stack the apples in the shape of a square pyramid with 6 layers, Starting the top layer, there is only one apple, the second layer has 4 apples, third has 9, and so on, a. write the rule for the number of apples in each layer b. How many apples are there in the stack?
- 16. Series If you add the terms in the sequence, the result of the expression is series
- 17. Find the series of, ... Sequence A 2, 4, 6, 8, 10, 12, 14, 16 Sequence B 3, 9, 15, 21, 27, 33
- 18. Using Summation Notation, we can also solve sequence Sequence A 2, 4, 6, 8, 10, 12, 14, 16 Sequence B 3, 9, 15, 21, 27, 33
- 19. Sequence and Series ordered set of mathematical quantities called terms Series is the sum of all terms in the sequence
- 20. Let's Get Involved on the Task! Answer page 11 - 12 on your book , Guided Practice A -
- 21. Asynchronous Task Check your Canvas Course and Check for the Published Assignment
- 22. Thank You for Listening!