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28 March, 20:50

two terms of an arithmetic sequence are a6 = 40 and a20 = - 16. write and explicit rule for the nth term

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  1. 28 March, 21:47
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    Tn = 64-4n

    Step-by-step explanation:

    The nth term of an AP is expressed as:

    Tn = a + (n-1) d

    a is the common difference

    n is the number of terms

    d is the common difference

    Given the 6th term a6 = 40

    T6 = a + (6-1) d

    T6 = a+5d

    40 = a+5d ... (1)

    Given the 20th term a20 = - 16

    T20 = a + (20-1) d

    T20 = a+19d

    -16 = a+19d ... (2)

    Solving both equation simultaneously

    40 = a+5d

    -16 = a+19d

    Subtracting both equation

    40 - (-16) = 5d-19d

    56 = - 14d

    d = 56/-14

    d = - 4

    Substituting d = - 4 into equation

    a+5d = 40

    a+5 (-4) = 40

    a-20 = 40

    a = 20+40

    a = 60

    Given a = 60, d = - 4, to get the nth term of the sequence:

    Tn = a + (n-1) d

    Tn = 60 + (n-1) (-4)

    Tn = 60 + (-4n+4)

    Tn = 60-4n+4

    Tn = 64-4n
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