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Math Help - Need help for systems and sequences

  1. #1
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    Post Need help for systems and sequences

    If Tn=(a+b)n-3,what is the common difference? What is t5?

    For the quadratic sequence where a= -2 andb=3, find the general term.Find t10 for the sequence.

    For the sequence x-2,2x-1,3x,.... Find the next two terms in the sequence. Find tn.

    How many terms are in the sequence -4,-16,-36,-64,.....-1764?

    Find two numbers whose sum is m and whose difference is n.

    Solve the system for x and y:ax-by=a2+b2
    x-y=2b
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  2. #2
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    Quote Originally Posted by cinbad
    If Tn=(a+b)n-3,what is the common difference? What is t5?
    Notice that,
    t_{n+1}=(a+b)(n+1)-3
    t_n=(a+b)n-3
    Thus,
    t_{n+1}-t_n=(a+b)(n+1)-3-[(a+b)n-3]
    Thus,
    t_{n+1}-t_n=(a+b)(n+1)-(a+b)n
    Thus,
    t_{n+1}-t_n=(a+b)(n+1-n)=(a+b)


    Quote Originally Posted by cinbad
    For the sequence x-2,2x-1,3x,.... Find the next two terms in the sequence. Find tn.
    Notice, you keep adding x+1
    Thus,
    t_1=(x-2)+0(x+1)
    t_2=(x-2)+1(x+1)
    t_3=(x-2)+2(x+1)
    ....
    t_n=(x-2)+(n-1)(x+1)

    Quote Originally Posted by cinbad
    How many terms are in the sequence -4,-16,-36,-64,.....-1764?
    This, is neither arithmetic nor geometric. I think you made a mistake somewhere.
    Quote Originally Posted by cinbad
    Find two numbers whose sum is m and whose difference is n.
    You have,
    \left\{\begin{array}{cc}x+y&=m\\x-y&=n\end{array}\right
    Add the two equations, to get,
    2x=m+n
    Subtract them to get,
    2y=m-n
    Thus,
    \left\{\begin{array}{cc}x=&\frac{m+n}{2}\\y=&\frac  {m-n}{2}\end{array}\right
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  3. #3
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    For the last question you want to solve, a\not= b
    \left\{\begin{array}{cc}ax-by=&a^2+b^2 \mbox{ (1)}\\x-y=&2b \mbox{ (2)}\end{array}\right
    Multiply equation (2) by a then subtract from (1),
    ay-by=a^2-2ab+b^2=(a-b)^2
    Thus,
    y(a-b)=(a-b)^2
    Thus,
    y=a-b
    Similarily,
    x=b-a
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  4. #4
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    Quote Originally Posted by cinbad
    ...

    How many terms are in the sequence -4,-16,-36,-64,.....-1764?
    Hello,

    the equation of this sequence is:
    a(n)=-(2n)^2

    1764=42^2 therefore you've got 21 summands.

    Greetings

    EB
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  5. #5
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    Quote Originally Posted by cinbad
    How many terms are in the sequence -4,-16,-36,-64,.....-1764?
    Notice that each term is divisable by 4. Thus the sequence is equivalent to
    -4[1, 4, 9, 16, ...441] = -4[1^2, 2^2, 3^2, ..., 21^2]. The second matrix puts the number of terms clearly at 21.

    Regards,

    Rich B.
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