Arithmetic Sequence.pptx

Arithmetic Sequence.pptx

• 1.
  Morning Drill Evaluate thefollowing: 1. y ÷2 + x ; x=1 and y=2 2. p2 + m ; m=1 and p=5 3. m + p ÷ 5 ; m=1 and p=5 4. z(x + y) ; x=6, y=8 and z=6 5. p3 + 10 + m ; m=9 and p=3
• 2.
  ARITHMETIC SEQUENCE Mr. Zaint HarbiA. Habal Teacher
• 3.
  ARITHMETIC SEQUENCE - Isa sequence where each succeeding term is obtained by adding a fixed number. The fixed number is called the common difference which is denoted as d.
• 4.
  What’s new Determine whetherthe sequence is arithmetic or not. If it is, find the common difference. 1. 2, 6, 10, 14, . . . 2. –4, 8, –16, 32, –64, . . . 3. 2, 1, 1/2, 1/4, 1/8, . . . 4. 20, 13, 6, –1, –8, . . . 5. 2, 2 1/2 , 3, 3 1/2, . . .
• 5.
  What I know? Givenby the arithmetic sequence 3, 7, 11, 15, … a. What is the common difference? b. How many terms will you find if you are going to evaluate a15? c. What is the value of the 1st term? 2nd term? 3rd term? 4th term? d. If the sequence will be continued, what do you think is the value of the tenth term? 15th term? 20th
• 6.
  Think-Pair-Share Example 1 Consider thesequence 3, 7, 11, 15, . . . , what is the 15th term in the given sequence? Example 2 What is the 15th term of the sequence 5, 3, 1, –1, –3, –5, . . .? Example 3 In the arithmetic sequence -3, 0, 3, 6, …, which term is equal to 138?
• 7.
  ARITHMETIC SEQUENCE To findthe next terms in an arithmetic sequence, we use the formula: 𝒂𝒏 = 𝒂𝟏 + 𝒏 − 𝟏 𝒅 Where; an – the last nth term a1 – the first term n – the number of terms in the sequence
• 8.
  Study the givenexamples below and identify if it is arithmetic or not. 1. 10, 13, 16, 19, … 2. 2, 6, 18, 54, … 3. 57, 49, 41
• 9.
  Example 1: Determine the10th term in the sequence 4, 6, 8, 10, … 𝒂𝒏 = 𝒂𝟏 + 𝒏 − 𝟏 𝒅 The first element / term: a1 = 4. The common difference: d = 2 The term: n = 10
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  Example 2: Find the7th term of an arithmetic sequence given the first three terms 2, 6, 10. Example 3: Find the 10th term of an arithmetic sequence given the first 4 terms 10, 19, 28, 37.
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  Seat Work /Assignment: 1. Find the 12th term of an arithmetic sequence whose first term is 38 and common difference of – 2. 2. Find the 15th term of the arithmetic sequence 2, 4, 6. 3. Find the 25th term of the arithmetic sequence 13, 16, 19, 22, …
• 12.
  Example 4: Form anarithmetic sequence with 1st term 3 and 7th term 15. Example 5: If the 6th term of an arithmetic sequence is 24 and the 12th term is 48, find the first term.
• 13.
  Hint: Find thecommon difference using the formula: 𝒅 = 𝒂𝒏−𝒂𝒎 𝒏−𝒎 where am is the first given term an is the last given term m is the position of am n is the position of an
• 14.
  Example 6: If a38= 140 and a51 = 192, what is a5? Example 7: What is the first 5 terms of an arithmetic sequence whose 23rd term is –107 and whose 55th term is –267?
• 15.
  What I know? Guessthe missing term on the following sequence then find the sum. 1. -1, ___, ___, ____, ___, 14 2. 14, ___, ___, ___, ___, ___, 86 The missing number/s is/are called the arithmetic mean/s of the two numbers.
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  ARITHMETIC MEAN - itis the terms between any two nonconsecutive terms of an arithmetic sequence.
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  ARITHMETIC MEAN Illustrative Example: Findtwo arithmetic means between 2 and 8. *Using d = 2, generate the next terms by adding “d” to the previous term.* So a2 = a1 + d and a3 = a2 + d which means
• 18.
  ARITHMETIC MEAN You mayuse the formula for the common difference to find the arithmetic mean. 𝒅 = 𝒂𝒏−𝒂𝟏 𝒏−𝟏 or 𝒅 = 𝒂𝒏−𝒂𝒎 𝒏−𝒎
• 19.
  Going back toWhat I know? Example 1: Guess the missing term on the following sequence then find the sum. 1. -1, ___, ___, ____, ___, 14 2. 14, ___, ___, ___, ___, ___, 86
• 20.
  Example: 2. Find thearithmetic mean of 7 and 15. 3. Find the four arithmetic means between 7 and -13.
• 21.
  Example 4: Find thesum of the first: a. five positive numbers b. ten positive numbers c. 20 positive numbers d. 100 positive even numbers
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  Example 5: Find thesum of the first 20 terms of an arithmetic sequence 2, 5, 8, 11, …
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  ARITHMETIC SERIES Arithmetic seriesis an indicated sum of the first n terms of an arithmetic sequence. The sum of n terms is denoted by Sn.
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  ARITHMETIC SERIES The formulain finding arithmetic series is 𝑺𝒏 = 𝒏 𝟐 (𝒂𝟏 + 𝒂𝒏) 𝑺𝒏 = 𝒏 𝟐 [𝟐𝒂𝟏 + 𝒏 − 𝟏 𝒅]
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  Example 4: Find thesum of the first: a. five positive numbers b. ten positive numbers c. 20 positive numbers d. 100 positive even numbers
• 26.
  Example 5: Find thesum of the first 20 terms of an arithmetic sequence 2, 5, 8, 11, … Example 6: Find the sum of the first 10 terms of the arithmetic sequence 4, 10, 16, 22, 28, …
• 27.
  Example 7: Find thesum of the first 30 multiples of 5. Example 8: Find the sum of the first 25 multiples of 3
• 28.
  Assignment: 1. If a38= 140 and a51 = 192, what is a1? 2. What are the two arithmetic means of the terms -8 and 100? 3. What is the sum of the first 24 terms of the arithmetic sequence: 4,8,12,16,…? 4. Find the sum of all odd integers from 10 to 100. 5. What is the 10th term of the arithmetic sequence -4, 1, 6, 11, …?