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Maaaaaaaath

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the first three terms of an arithmetic sequence are x-2;2x+6 and 4x-8 respectively..determine.....(1)x (2) the 20th term (3) the sum of the first 20 terms of the sequence

  • Maaaaaaaath - ,

    1)T2-T1=T3-T2
    2x+6-(x-2)=4x-8-(2x+6)
    2x+6-x+2=4x-8-2x-6
    x+8=2x-14
    x=22
    2)substitute for x:
    1st term:x-2=22-2=20
    2nd term:2x+6=2(22)+6=44+6=50
    3rd term:4x-8=4(22)-8=88-8=80
    now we look for the constant difference(d):
    T2-T1=50-20=30
    T3-T2=80-50=30
    So d=30
    Tn=an+(n-1)d
    T20=20(20)+(20-1)(30)
    T20=400+(19)(30)
    T20=400+570
    T20=970
    3)Sn=n/2(2a+(n-1)d)
    S20=20/2[2(20)+(19)(30)]
    s20=10(40+570)
    s20=10(610)
    s20=6100

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