the 7th term of ap is -4 and its 13 term is -16 find the ap

Question

the 7th term of ap is -4 and its 13 term is -16 find the ap

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Aubrey 2 months 2021-11-28T15:45:05+00:00 2 Answers 0 views 0

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    0
    2021-11-28T15:46:16+00:00

    Answer:

    The Answer is,

    a=8

    d=(-2)

    The formula for nth term is,

    an=a+(n-1)d

    Hence substituting 7 in the place of n, we get,

    a7=a(7-1) d

    a7=a+6d…… (eq-1)

    Similarly, Substituting 13 in the place of n, we get,

    a13=a+(13-1)d

    a13=a+12d…… (eq-2)

    Subtracting Equation (2) from (1), we get,

    -6d=12,

    d=12/-6

    d=-2

    Hence substituting d=-2 in any of the equations

    we get,

    a=8

    Hence the A. P is,

    8,6,4,2,0,-2, -4, -6…..

    0
    2021-11-28T15:46:53+00:00

    Answer:

    Step-by-step explanation:

    given that

    7th term is -4,so

    a +6d =-4 let this be equation 1

    and

    a +12d = 13 let this be equation 2

    adding equation 1 and 2 we get

    a+6d + a +12 d = -4 – 16

    2a + 18d  = -20

    dividing the equation by 2 we get

    a +9d =-10

    therefore the 8th term is -10

    d = 8th term -7th term

    d= -10 +4

    d= -6

    substituting in eq 1 we get

    a+6(-6) =-4

    a-36=-4

    a= 32

    a+d = 32-6=26

    a+2d = 32-12 =20

    a+3d =32-18= 14

    therefore the AP is 32,26,20.14……….

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