6.1 quadratic sequences and tables
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This document discusses quadratic sequences and functions. It defines quadratic sequences as having a common second difference, unlike linear sequences which have a common first difference and exponential sequences which have a common ratio. Examples are provided to demonstrate how to find the second difference and next term of quadratic sequences. The document also discusses classifying sequences as linear, exponential, quadratic, or neither based on their patterns of differences or ratios.
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Arithmetic progression
Arithmetic progression
For class 10.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
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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.
Generating Patterns and arithmetic sequence.pptx
The given document discusses arithmetic sequences and their properties. It defines an arithmetic sequence as a sequence where each term is obtained by adding a fixed number (called the common difference) to the preceding term. It provides the formula for calculating the nth term of an arithmetic sequence as an = a1 + d(n - 1), where a1 is the first term and d is the common difference. Examples are provided to determine if a sequence is arithmetic or not based on this definition and formula. The document also contains practice problems asking users to find missing terms, identify patterns, and calculate specific terms of arithmetic sequences.
Math Gr4 Ch6
Let's analyze the pattern to write a rule.
The cost increases by $2 each time.
Rule: Cost = $5 + 2x
To find the cost for 7 people:
Cost = $5 + 2(7) = $5 + 14 = $19
The cost for 8 people is $5 + 2(8) = $5 + 16 = $21
So the amount earned for 7 and 8 people is $19 and $21.
The answer is A.
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
A sequence is a list of ordered numbers, while a series occurs when the terms of a sequence are added together. Sigma notation, also called summation notation, is used to write out series concisely. It involves writing the summation symbol followed by the pattern rule for the terms, along with the lower and upper limits of the series. There are special formulas that can be used as shortcuts for finding the sums of common series, such as the formulas for the sum of the first n positive integers and the sum of the first n squares.
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
A sequence is a list of ordered numbers, while a series occurs when the terms of a sequence are added together. Sigma notation, also called summation notation, is used to write out series concisely. It involves writing the summation symbol followed by the pattern rule for the terms, along with the lower and upper limits of the series. There are special formulas that can be used as shortcuts for finding the sums of common series, such as the formulas for the sum of the first n positive integers and the sum of the first n squares.
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES (1).ppt
A sequence is a list of ordered numbers, while a series occurs when the terms of a sequence are added together. Sigma notation, also called summation notation, is used to write out series concisely. It involves writing the summation symbol followed by the pattern rule for the terms, along with the lower and upper limits of the series. There are special formulas that can be used as shortcuts for finding the sums of common series, such as the formulas for the sum of the first n positive integers and the sum of the first n squares.
Patterns, sequences and series
The document discusses arithmetic and geometric sequences and series. It defines arithmetic and geometric sequences, and provides the formulas for calculating the nth term of each type of sequence. Specifically, it states that the formula for the nth term of an arithmetic sequence is Tn = a + (n-1)d, where a is the first term and d is the common difference. The formula for the nth term of a geometric sequence is Tn = arn-1, where a is the first term and r is the common ratio. The document also provides examples of using these formulas to find terms, common differences or ratios, and to write the formulas for given sequences.
Variability
The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.
January 29 30
The document provides practice problems on simplifying monomial expressions and dividing monomials. It begins with examples of dividing monomials using the property that when dividing powers with the same base, you subtract the exponents. It then provides practice problems for students to divide monomial expressions and simplify expressions using exponent properties. Sample problems are worked through step-by-step as examples.
Patterns in Sequences
Sequence
Patterns in Sequences
General Term/Rule
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ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES (1).ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES (1).ppt
ALLIED MATHEMATICS -II UNIT IV & UNIT V SEQUENCES AND SERIES.ppt
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6.6 quadratic formula
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4.1 trig ratios
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R.1 simplifying expressions
Algebraic expressions contain numbers, variables, and operators and can be simplified using the distributive property and by combining like terms. The document provides examples of algebraic expressions that can be simplified by first distributing all terms inside parentheses and then combining like terms, such as 3(4n + 2) + n, which is simplified to 12n + 6 + n = 13n + 6.
10 4 solving trig equations
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7 3 multiplying polynomials
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2) It derives formulas that relate trig functions of double and half angles to trig functions of the original angle, such as sin(2x) = 2sin(x)cos(x) and sin(x/2) = ±√(1-cos(x))/2.
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6.7 other methods for solving
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10 2 sum and diff formulas for tangent
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6.1 quadratic sequences and tables
- 1. Unit 6 – Quadratic Functions 6.1 Quadratic Sequences & Tables
- 2. Sequence Review Remember: Linear Sequences – ◦ Have a common difference ◦ (subtracting consecutive terms gives same # each time) Exponential Sequences – ◦ Have a common ratio ◦ (dividing consecutive terms gives same # each time)
- 3. Quadratic Sequences Quadratic Sequences – ◦ Have a common 2nd difference Example: 1, 4, 9, 16, 25, 36, … 2nd Difference = 2 +3 +5 +7 +9 +11 +2 +2 +2 +2
- 4. Example: Find the 2nd difference and the next term for: 3, 7, 12, 18, 25, …
- 5. Example: Find the 2nd difference and the next term for: -6, 5, 40, 99, 182, …
- 6. You Try! Find the 2nd difference and the next term for: 12, 56, 130, 234, 368, …
- 7. Classifying Sequences Determine if each sequence is linear, exponential, quadratic, or neither? 19, 13, 7, 1, -5, … 2, 6, 18, 54, 162, … -12, -11, -7, 0, 10, …
- 8. You Try! Determine if each sequence is linear, exponential, quadratic, or neither? 8, 13, 28, 33, 48, … 7, 70, 169, 304, 475, …