Sequences and series
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The document contains information about arithmetic and geometric sequences. It defines an arithmetic sequence as one where each term is found by adding the same number to the previous term, called the common difference. A geometric sequence is one where each term is found by multiplying the previous term by the same number, called the common ratio. Examples are worked through and questions are asked about finding the next term in various sequences.
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INTERACTIVE MULTIMEDIA on ARITHMETIC SEQUENCE_SIM FOR MATH GRADE 10.pdf
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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
Subtraction of Integers.pptx
This document provides examples and rules for subtracting integers:
1) To subtract integers, add the opposite of the subtrahend to the minuend. For example, 3 - (-5) = 3 + 5 = 8.
2) Examples are worked out following this rule, such as -24 - 9 = -24 + (-9) = -33.
3) Real-life examples are presented and solved, such as finding the change received from a 200-peso bill when vegetables cost 96 pesos.
Geometric sequence day 1
This document discusses geometric sequences. A geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a constant ratio. Examples of geometric sequences are provided along with their common ratios. Students are asked to determine whether sequences are geometric or not, and for geometric sequences to provide the common ratio. The key differences between arithmetic and geometric sequences are that arithmetic sequences involve adding a fixed difference between terms while geometric sequences involve multiplying terms by a constant ratio.
Arithmetic Sequence
This document defines arithmetic sequences and provides examples and explanations of key concepts such as the common difference, finding specific terms, finding sums of terms, and solving word problems involving arithmetic sequences. Key points covered include defining an arithmetic sequence as a sequence where each term is obtained by adding a constant to the preceding term, using the formula an = a1 + (n-1)d to find the nth term, and the formulas Sn = n(a1 + an)/2 and Sn = n(n-1)d/2 to find the sum of the first n terms. Examples of finding missing terms, common differences, and sums are worked through.
8.3 factorisation lesson
The document provides information about factorizing algebraic expressions:
- It discusses factors and multiples, explaining what they are and providing examples of finding factors and multiples.
- It introduces factorizing algebraic expressions by taking out common factors. Examples are given of factorizing expressions like 3x^2 + 5x.
- Students are given practice problems to factorize expressions involving variables like x, y, a. They are also given practice finding the highest common factor of numbers and algebraic expressions.
Practice questions and tips in business mathematics
The document provides practice questions and tips for business mathematics exams. It includes 20 sample questions covering topics like ratios, percentages, time/work problems, profit/loss, and series sums. The questions are multiple choice with explanations provided for the answers.
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INTERACTIVE MULTIMEDIA on ARITHMETIC SEQUENCE_SIM FOR MATH GRADE 10.pdf
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Practice questions and tips in business mathematics
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Sequences and series
- 1. Examine the following lists below and group the lists into three: -2,-3,-4,-5,-6 2,7,8,11,19 3,6,9,12,15 1,3,9,27,81 0,1.1,4,5,7.7
- 2. What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, +4 8,+4 12 +4 16,+4 20………….. ,
- 3. What is the common difference? The difference between each number. This determines what is added to each previous number to obtain the next number. 4, 8, 12, 16, 20………….. 4 is the common difference
- 4. What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. 3,x3 9,x3 27x3 81, 243………….. , x3
- 5. What is the common ratio? The number used to multiply by each previous number to obtain the next number. 2, 8, 32, 128, 512………….. 4 is the common ratio
- 7. Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference
- 8. Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio
- 9. What is the next term in this sequence? x4 x4 x4 x4 5, 20, 80, 320 , _____ 1,280
- 10. What is the next term in this sequence? -6 -6 -6 -6 5, -1, -7 -13 , _____ -19
- 11. What is the next term in this sequence? X-2 X-2 X-2 X-2 -3, 6, -12, 24 , _____ -48
- 12. What is the next term in this sequence? +20 +20 +20 +20 -400,-380,-360,-340 , ____ -320
- 13. What is the next term in this sequence? -25 -25 -25 -25 100, 75, 50 , 25____ 0
- 14. What is the next term in this sequence? x-4 x-4 x-4 x-4 12, -48, 192 , -768____ 3,072