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

Question

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

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Melody 1 hour 2021-10-14T11:59:22+00:00 1 Answer 0

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    2021-10-14T12:00:50+00:00

    Answer:

    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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