maths

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three number form an arithmetric sequence. Their sum is 24.
A)If 'a' is the first number and 'd' the common difference, show that a+d=8
B)If the first number is decreased by 1 and the second number by 2, the three numbers then form a geometric sequence. Find the three terms.

  • maths -

    your last 3 postings all deal with the basic definitions of sequences and series and involve translating the English statements into mathematical expressions.

    Why don't you show me what you have done for this one so far, and I will gladly help you further.

  • maths -

    ok cool... a) S/n=n/2 [2a+(n-1)d]
    24=3/2[2a+2d]
    48=3[2a+2d]
    16=2a+2d
    8=a+d
    B)i don't know from here hey...
    my name is marco

  • maths -

    ok Marko, it would have been easier to just do this
    a + a+d + a+2d = 24
    3a + 3d = 24
    a + d = 8

    b) so now we know that a = 8-d

    "If the first number is decreased by 1" so term1 = a-1
    " the second number by 2" , so term2 = a+d - 2

    our new terms are then
    t1 = a-1 = 8-d - 1 = 7-d
    t2 = a+d-2 = 8-d-d-2 = 6
    t3 = a+2d = 8-d + 2d = 8+d

    now these form a GS
    then

    6/(7-d) = (8+d)/6

    take over.

  • correction - maths -

    near the end I had a typo but it did not cause an error

    t2 = a+d-2 = 8-d-d-2 = 6 should have been

    t2 = a+d-2 = 8-d+d-2 = 6

  • maths -

    ok thx.. i got 36=(8+d)(7-d)
    36= 56-8d+7d-d squared
    36=-d^2-d+56
    d^2+d-56+36=0
    d^2+d-20=0
    (d-4)(d+5)=o
    d=4 d=-5
    therefore
    T1=3
    T2=6
    T3=12
    and
    T1=12
    T2=6
    T3=3

  • maths -

    Nice, see how easy they are ?

  • maths -

    ya thx a ton

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