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    Arithmetic (Q1W3D1)

    Uploaded by

    Justine Benedick M Dizon
    This document discusses arithmetic means of arithmetic sequences. It defines arithmetic mean as the terms between any two non-consecutive terms of an arithmetic sequence. The formula for an arithmetic sequence is provided, along with steps to solve problems involving arithmetic means: 1) use the formula to find the common difference, and 2) add the common difference to the preceding term to find missing terms. Examples are provided to insert arithmetic means into sequences and find another term given the arithmetic mean between two terms.

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    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd

    Arithmetic (Q1W3D1)

    Uploaded by

    Justine Benedick M Dizon
    20 views14 pages
    This document discusses arithmetic means of arithmetic sequences. It defines arithmetic mean as the terms between any two non-consecutive terms of an arithmetic sequence. The formula for an arithmetic sequence is provided, along with steps to solve problems involving arithmetic means: 1) use the formula to find the common difference, and 2) add the common difference to the preceding term to find missing terms. Examples are provided to insert arithmetic means into sequences and find another term given the arithmetic mean between two terms.

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    Arithmetic(Q1W3D1)

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    This document discusses arithmetic means of arithmetic sequences. It defines arithmetic mean as the terms between any two non-consecutive terms of an arithmetic sequence. The formula for an arithmetic sequence is provided, along with steps to solve problems involving arithmetic means: 1) use the formula to find the common difference, and 2) add the common difference to the preceding term to find missing terms. Examples are provided to insert arithmetic means into sequences and find another term given the arithmetic mean between two terms.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    20 views14 pages

    Arithmetic (Q1W3D1)

    Uploaded by

    Justine Benedick M Dizon
    This document discusses arithmetic means of arithmetic sequences. It defines arithmetic mean as the terms between any two non-consecutive terms of an arithmetic sequence. The formula for an arithmetic sequence is provided, along with steps to solve problems involving arithmetic means: 1) use the formula to find the common difference, and 2) add the common difference to the preceding term to find missing terms. Examples are provided to insert arithmetic means into sequences and find another term given the arithmetic mean between two terms.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 14

    Arithmetic Mean

    Quarter I Week 3

    GERALD C. MANOLID
    Subject Teacher
    Answer
    Activity 5 Activity 6
    1. The relationship between the sum of the
    A. terms and the sum of the first and last terms
    of an arithmetic sequence is that you can get
    1. 18, 30, 42 the sum by multiplying the first and last
    terms' sum by half to get the total. This is
    2. 55, 42, 29, 16 because finding the sum of the terms is
    easier when you start with the first and last
    3. -1, 2, 5 terms.
    2.
     
    4. 1, 3/2
    B.1. 0 2. x=6
    OBJECTIVES
    The learner will be able to:
     determines arithmetic means of an arithmetic sequence.
     solves problems on arithmetic sequence involving
    arithmetic means.
     cooperate patiently with the groupmates in doing their
    assigned tasks.
    DEPARTMENT OF EDUCATION
    Who can write the assignment and its answer on
    the board?
    1. 6 and 54 [ 3 ]
    2. 68 and 3 [ 4 ]
    Questions:
    1. What is arithmetic means?
    2. How did you get the 3 arithmetic means
    between 6 and 54?
    DEPARTMENT OF EDUCATION
    Arithmetic Mean
    Are the terms between any two nonconsecutive terms of
    an arithmetic sequence
    Formula: wherein:
    𝑎1=1 𝑠𝑡 𝑡𝑒𝑟𝑚 𝑎 𝑛=𝑛𝑡h 𝑡𝑒𝑟𝑚
    𝒂 𝒏= 𝒂𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝑛=𝑛𝑜.𝑜𝑓 𝑡𝑒𝑟𝑚 𝑑=𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
    Steps in solving the arithmetic mean
    1. Using the formula of arithmetic sequence solve for
    the value of the common difference
    2. To get the value of the missing term add the common
    difference and the value before the missing term.
    Activity: Work in Pair!
    1. Insert 6 arithmetic means
    between 5 and 61 .
    2. Insert 5 arithmetic means
    between 66 and -6.
    DEPARTMENT OF EDUCATION
    Insert six arithmetic means between 5 and 61.
    5, ___,
    13, ___, 37, ___,
    29, ___,
    21, ___, 53, 61,
    45, ___,
    1 2 3 4 5 6 7 8
    𝑎 6=𝑎5 + 𝑑
    Given: 𝑎 6=37+8
    𝑎 1=5 𝑛=8¿ 7 𝑑¿ 56
    𝑎 𝑛=61 𝑑= ? 77 𝑎6=45
    𝒅 =𝟖 𝑎 7=𝑎 4 +𝑑
    Formula:
    Arithmetic Mean: 𝑎 7=45+ 8
    𝒂 𝒏=𝒂𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝑎 2=𝑎1 +𝑑 𝑎 4 = 𝐴 3 +𝑑 𝑎 5=53
    Solution 𝑎 2=5+ 8 𝑎 4 =21+8
    :
    61=5 + ( 8 −1 ) 𝑑 𝑎 2=13 𝑎 4 =29
    61=5 + ( 7 ) 𝑑 𝑎 3=𝑎2 + 𝑑 𝑎 5= 𝐴 4 + 𝑑
    7 𝑑=61− 5 𝑎=13+ 8 𝑎5=29+ 8
    𝑎=21 𝑎5=37
    Insert five arithmetic means between 66 and -6.
    54 ___,
    66 ___, 30 ___,
    42 ___, 6
    18 ___, -6,
    1 2 3 4 5 6 7
    , 𝑎 6=𝑎5 + 𝑑
    Given: 𝑎 6=18− 12
    𝑎 1=66 𝑛=¿ 7 ¿
    6 𝑑 −72
    𝑎 6= 6
    𝑎𝑛=− 6 𝑑= ?
    𝒅=−𝟏𝟐
    Formula:
    Arithmetic Mean:
    𝒂 𝒏=𝒂𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝑎 2=𝑎1 +𝑑 𝑎 4 =𝑎 3 +𝑑
    Solution 𝑎 2=66 − 12 𝑎 4 =42 − 12
    :
    −6=66 + ( 7 −1 ) 𝑑 𝑎 2=54 𝑎 4 =30
    − 6=66 + ( 6 ) 𝑑 𝑎 3=𝑎2 + 𝑑 𝑎 5=𝑎4 + 𝑑
    6 𝑑=−66 − 6 𝑎 3=54 −12 𝑎 5=30 − 12
    𝑎 3= 42 𝑎 5=18
    Try to solve these problems alone:
    1. The arithmetic mean between
    two terms in an arithmetic
    sequence is 39. If one of these
    terms is 32, find the other term.

    DEPARTMENT OF EDUCATION
    What is your interpretation to
    this problem?

    How are you going to find the


    other term?
    DEPARTMENT OF EDUCATION
    What is your interpretation to
    this problem?
    The other term can be found by getting first the common
    difference like, 39-32 = 7
    since 39 is the arithmetic mean bet.2 terms so 39 is next
    to 32 then 39 + 7 = 46.
    DEPARTMENT OF EDUCATION
    How are you going to find the
    other term?
    The other term then is 46 and the
    sequence is 32, 39, 46,…

    DEPARTMENT OF EDUCATION
    Arithmetic Mean
    Are the terms between any two nonconsecutive terms of
    an arithmetic sequence
    Formula: wherein:
    𝑎1=1 𝑠𝑡 𝑡𝑒𝑟𝑚 𝑎 𝑛=𝑛𝑡h 𝑡𝑒𝑟𝑚
    𝒂 𝒏= 𝒂𝟏 + ( 𝒏 − 𝟏 ) 𝒅 𝑛=𝑛𝑜.𝑜𝑓 𝑡𝑒𝑟𝑚 𝑑=𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
    Steps in solving the arithmetic mean
    1. Using the formula of arithmetic sequence solve for
    the value of the common difference
    2. To get the value of the missing term add the common
    difference and the value before the missing term.
    THANK YOU

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