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Math Help - geomertric and arithmetric sequences

  1. #1
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    geomertric and arithmetric sequences

    a geometric sequence of posotive terms has first term 2 and the sum of the first three terms is 266 calculate the common ratio

    an arithmetric sequense A has first term a and a common difference of 2 and a geometric sequence B has first term a and common ratio 2. the first four terms of each sequence have the same sum. obtain the value of a

    any help would be appreciated
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  2. #2
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    Quote Originally Posted by hmmmm View Post
    a geometric sequence of posotive terms has first term 2 and the sum of the first three terms is 266 calculate the common ratio
    2 + 2r + 2r^2 = 266

    solve for r


    an arithmetric sequense A has first term a and a common difference of 2 and a geometric sequence B has first term a and common ratio 2. the first four terms of each sequence have the same sum. obtain the value of a
    a + (a+2) + (a+4) + (a+6) = a + 2a + 4a + 8a

    solve for a
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  3. #3
    MHF Contributor red_dog's Avatar
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    1) a_1=2, \ a_2=2r, \ a_3=2r^2

    a_1+a_2+a_3=266\Rightarrow r^2+r-132=0 and you have to solve the quadratic.

    2) a+(a+2)+(a+4)+(a+6)=a+2a+4a+8a

    Now find a.
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