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This document contains three sections that provide arithmetic and geometric sequence problems to solve. Section I contains problems about finding the differences in given arithmetic sequences and determining if other sequences are arithmetic. Section II contains additional arithmetic sequence problems involving finding terms and inserting means. Section III contains problems about sums of money in taxes, rational numbers as ratios, and finding terms in geometric sequences given initial terms or common ratios.
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Here are the steps to solve the problems:
1. Given: a1 = 15 seats, d = 3 additional seats per row, n = 40 rows
Solve for an:
an = a1 + (n-1)d
= 15 + (40-1)3
= 15 + 117
= 132
Solve for S40:
S40 = n/2(a1 + an)
= 40/2(15 + 132)
= 40/2(147)
= 2940
2. Given: a1 = Php 1000, d = Php 300 additional sales per week, n = 15 weeks
Solve for an:
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https://tinyurl.com/y9muob6q
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https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
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https://tinyurl.com/ybo27k2u
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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 sequences and their properties. It defines an arithmetic sequence as a sequence where the difference between consecutive terms is constant. It provides the formula for the nth term of an arithmetic sequence as an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. It gives examples of finding specific terms and summarizing sequences. It also discusses the arithmetic mean and arithmetic sum formulas.
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If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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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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The document discusses arithmetic and geometric sequences and their key characteristics. An arithmetic sequence has a common difference, while a geometric sequence has a common ratio. Several example sequences are provided and the reader is asked to identify whether they are arithmetic, geometric, or neither and determine their common differences or ratios.
SimplifyingExpressionsAIREOCQuestions
1) The document provides 11 multiple choice questions about simplifying algebraic expressions.
2) The questions cover topics like identifying equivalent expressions, combining like terms, and distributing terms.
3) Sample student answers are provided that explain the reasoning for each response.
sum of arithmetic sequence s
Here are the steps to solve the problems:
1. Given: a1 = 15 seats, d = 3 additional seats per row, n = 40 rows
Solve for an:
an = a1 + (n-1)d
= 15 + (40-1)3
= 15 + 117
= 132
Solve for S40:
S40 = n/2(a1 + an)
= 40/2(15 + 132)
= 40/2(147)
= 2940
2. Given: a1 = Php 1000, d = Php 300 additional sales per week, n = 15 weeks
Solve for an:
an = a1 +
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GRADE 10 ARITHMETIC.pptx
1. The document provides lesson content on arithmetic sequences, including definitions, examples, and formulas.
2. Students are expected to illustrate arithmetic sequences, determine terms and sums of sequences.
3. The lesson covers identifying patterns in sequences, defining arithmetic sequences and common differences, and finding missing terms and general formulas for arithmetic sequences.
Arithmetic Sequence.pptx
The document discusses arithmetic sequences and series, including how to determine if a sequence is arithmetic, how to find subsequent terms using the common difference, and how to calculate the sum of the first n terms of an arithmetic series using the arithmetic series formula. Examples are provided to illustrate how to identify arithmetic sequences, calculate missing terms, find common differences, and compute sums of arithmetic series.
Q1_W6_Geometric Sequence Part I.pptx
This document provides information about geometric sequences. It defines a geometric sequence as a sequence where each term is obtained by multiplying the preceding term by a common ratio. The key points are:
- A geometric sequence is defined by a common ratio r that is used to multiply the preceding term to obtain the next term.
- To find missing terms, the common ratio r is used to multiply or divide the preceding term.
- The formula for the nth term an of a geometric sequence is an = a1rn-1, where a1 is the first term and r is the common ratio.
- Examples are provided to demonstrate finding missing terms and calculating the nth term using the formula.
- The
Sequence and series
The document discusses arithmetic sequences and series. An arithmetic sequence is a sequence where the difference between successive terms is constant. The nth term can be calculated using the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. The sum of an arithmetic sequence is called an arithmetic series, which can be calculated using the formula Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
Successful Minds,Making Mathematics number patterns &sequences Simple.
This document provides information about number patterns and sequences. It discusses arithmetic sequences where the difference between consecutive terms is constant, and quadratic patterns where the second differences are constant. Examples are provided to demonstrate how to determine the general term of a sequence from a given pattern. Practice problems with solutions allow the reader to apply the concepts to find missing terms, general terms, and values of specific terms.
Ebook 1
This document provides information about number patterns and sequences. It discusses arithmetic sequences where the difference between consecutive terms is constant, and quadratic patterns where the second differences are constant. Examples are provided to demonstrate how to determine the general term of a sequence from a given pattern. Practice problems with solutions allow the reader to apply the concepts to find missing terms, general terms, and values of specific terms.
X maths 1
1. The document discusses strategies for students to score 10/10 grade in mathematics. It recommends practicing previous year question papers to understand concepts better.
2. It provides two sample question papers containing math problems like addition, subtraction, multiplication and division of integers, fractions and decimals. It notes that there are extra marks questions in both papers.
3. Studying the question papers carefully and understanding the logic behind extra marks questions will help students solve similar questions correctly and score full marks.
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Grade 10 Math Module 1 searching for patterns, sequence and series
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Successful Minds,Making Mathematics number patterns &sequences Simple.
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A
- 1. I. A. Find the difference of each arithmetic sequence. 1. 5, 8, 11, 14,... 2. 4, 14, 24, 34, 44,… 3. 9, 15, 21, 27,…. 4. 7, 2, -3, -8,….. 5. 7, 14, 21, 28,… B. Tell if the sequence is arithmetic. Write AS if ARITHMETIC, and mark X if NOT. 1. 1, 1, 2, 3, 5, 8, 13,…. 2. 1, 3, 5, 7, 9,…… 3. 1, 2, 4, 8, 16,….. 4. 2, 6, 10, 14, 18,…. 5. 1, 2, 3, 4, 5, 6,…. II. Answer the ff. 1. Find the difference in the arithmetic sequence. 1, 4, 7, 10, 13, 16,… 2. Find the difference in the arithmetic sequence 1, ½, 0, -1/2,… 3. Give the formula used in arithmetic sequence finding any terms. 4. Insert 3 arithmetic means between 7 and 23. 5. Find the 17th of the sequence 7, 10, 13, 16,… 6. Find the formula of the sequence 3, 5, 7, 9,… 7. Insert 2 arithmetic means between 11 and 21. 8. Find the arithmetic mean between 34 and 50. 9. Solve: t6= 19 d= 3 n=6 Find: t1 and t10. 10. Insert 3 arithmetic means between 13 and 61. III. Solve 1. There are 45 chairs in a triangular library. The first row has 13 chairs, 2nd row has 11 chairs, 3rd row has 9 chairs, and so on. How many rows the library has? Write the sequence. (4 pts.) 2. A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats are in the theater? Write the sequence. (6 pts.)
- 2. I. Write geometric if GEOMETRIC sequence and give the common ratio. Write NOT if the sequence is not geometric. 1. 2, 4, 8, 16, ….. 2. 18, 12, 8,…. 3. 1, -3, 9, -27, …. 4. 2, 6, 18, 54, … 5. 2, 5, 6, 8,… 6. 2, 4, 8, 16,…. 7. 1, 3, 6, 10,….. 8. 1.5, 3, 6, 12,…. 9. 1, ½, ¼, 1/8, 1/16,…. 10. 1, -1, 1, -1, 1,….. II. Answer the ff. 1. Give the 10th term of the geometric sequence if the 6th term is 90 and a common ratio of 3. 2. What is the common ratio of the sequence 4, 2, 1, 0.5, 0.25,….. 3. Give the general formula for geometric sequence. 4. Give the formula for geometric series. If r>1 5. If r<1 6. Find the sum if a1= 5 r=2 n=10 Give the first 4 terms of the ff. 7. 2n-1 8. 3(2)n-1 9. ½(-2)n-1 10. 27(1/3)n-1 III. Solve 1. How much is going to taxes? Suppose that we track a tax refund of $100. Each time money is spent 8% goes towards taxes and the rest gets spent again. How much of the original $100 will go back to taxes. 2. write the rational number 0.9717171... as a ratio of two positive integers. 3. Find r given that a1 = 10 and a20 = 10-18 4. Find a20 given that a3 = 1/2 and a5 = 8 5. Write the rational number 5.31313131... as the ratio of two integers. 6. Given the terms a10 = 3 / 512 and a15 = 3 / 16384 of a geometric sequence, find the exact value of the term a30 of the sequence.