Semi-Detailed Lesson Plan

Lesson Plan in Mathematics

I. Objective

At the end of the lesson the students are expected to:

l   Differentiate arithmetic sequence from arithmetic series

l   Relate arithmetic sequence and arithmetic series in real life problems

l   Solving arithmetic sequence and arithmetic series

II. Subject Matter

Topic : Arithmetic Sequence and Arithmetic Series

Reference : Mathematics III (IMC,1990)

http://www.khanacademy.org/video?v=Uy_L8tnihDM

https://youtu.be/stFjYpglm0o

Materials : Projector, strips/cards

III. Instructional Procedure

A. Review

What is sequence ….

B. Motivation

Students will be group into 2…Each group will be given strips/cards to analyze and organize the meaning and terms and explain the difference of the two terms with the help of it’s examples in where they also have to puzzled out. Teams who failed must face it’s consequence.

C. Lesson Proper

1. (PPT) Arithmetic Sequence

Consider these four sequence. Find the next three terms

A. -2, 2, 6, …                                                        C. -4, -10, -16, …

B. 8, 13, 18. 23, …                                                D. 1/8, 1/16, 1/32,...

In each sequence , how did you get the next terms?

            Sequence is where each succeeding term is obtained by adding a fixed  number  is called an

     arithmetic sequence. This fixed number is the constant difference d between two succeeding

terms.

     The term of the sequence can then be expressed  this way;

             a₁ = a₁+ 0d,  a₂ = a₁ + d,  a₃ = a_{1 +}  2d , .... a_n = a₁ + (n-1)d

             Any arithmetic  sequence is defined by the function given as a_n = a₁ + (n-1)d

   Example 1

            Find the 100 term of the arithmetic sequence for which the first term is 7 and d=5

            a_n = a₁ + (n-1)d

            a₁₀₀ =  7 + (100-1)5

            a₁₀₀ =  7 + (99)5

            a₁₀₀ =  7 + 495

            a₁₀₀ =  502

Example 2 (board work)

            In the arithmetic sequence for 1, 5, 9, 13, ... which  term is equals to 153 ?

            a₁  = 1 , a_n = 153 , d=4

            a_n = a₁ + (n-1)d

            153 = 1 + (n-1) 4

            153 = 1 + 4n -4

            153-1+4 = 4n

            156 = 4n

            n= 39

Example 3

            Simon has a piggy bank he dropped $ 1.00 on May 1, $1.75 on May 2, $2.50 on May 3 and so

     until the last day of May. How much did he drop in his piggy bank on May 19 ?

             a_n = a₁ + (n-1)d

            a₁₉ = 1+ (19-1)0.75

            a₁₉ = 1+ (18)0.75

            a₁₉ = 1+ 13.50

            a₁₉ = 14.50

2. (PPT) Arithmetic Series

     Play video

     Arithmetic series is an indicated sum of the first n terms of an arithmetic sequence. The sum of n

     denoted b S_n

     Do you understand arithmetic series now?

     Here’s some more  example to understand it better

 Example 2.2

     What is the sum of all poitive integers less than 300 that are multiples of 7

Ø The multiples of 7 form an arithmetic sequence such that 7 is the least positive integer multiple or a₁  = 7 and d = 7

Ø To get the S_n  find the nthe number of multiples of 7 that are less than 300. Three hundred is not a multiple of 7. The largest multiple of 7 less than 300 is a_n  < 300 then

            7+(n-1)7<300

            7+7n-7<300

            7n/7<300/7

            n<42.85

since n is an integer, n =42. Therefore, there are 42 positive integers that less than 300 which are multiples of 7. The largest of these multiple is a_{42 and}

             a₄₂ = 7+ 41(7)

                 = 249

The series formed is 7+14+21+28+...294 using the formula

S_n  =  n/2 (a_1|+ a_n)

S_n  = 42/2 (7+294)

     =6321

  Example 2.3 (Board work)

          An employee has a salary of $35,500 per year. The employee is promised a $ 2,750 raise each

         subsequent year over an 8 year period.

         a₁ = 35,500 , d= 2,750 , S₈ =? , n=8 , a₈  =?

        a₈  =35,500 + (8-1)2750

             = 35,500+7(2750)

             = 54,750

         S₈ = 8/2(35,500+54,750)

             = 361,000

    D. Generalization

         So now how do arithmetic series differ from sequence?

        Does solving both  isn’t hard enough specially with word problem?

        What’s the importance of this in our daily lives?                                                                                  

IV. Evaluation

A.      Find the term indicated in each of the following sequences.

  1. 9, 27, 81, ..                                                 18th term

  2.1/8, 1/4, 3/8, 1/2 , ...                                                        17th term

  3.How many numbers less than 400 but greater than 10 are divible by 7 ? Find the 20th to the 30th 

   terms of the resulting sequence.

 4. in the arithmetic sequence -3, 0, 3,6,.. , which term equals =138?

 5.Find the arithmetic sequence whose 10th term is and and 20th term is

   B. Find the sum of the terms in arithmetic sequences for the numbers terms indicated

 1.2+5+8+11, ...                                                                    30 term

 2.5+10+15+20,...                                                                 100 term

 3.What is the sum of all positive integers between 29 and 210 that are divisible by 4?

 4.Lee earned $240 in the forst week, $350 in the second week and $460 in the third week, and so

 on. How much did he earn in the first five weeks?

 5. Find the sum of the first counting numbers.

V. ASSIGNMENT

     Research about geometric sequence and series. Write down atleast 2 examples and must have a word problem each.