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Math Help - Question about geometric sequence

  1. #1
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    Question about geometric sequence

    I want to know how I can solve this question:
    IfYnis a geometric sequence such that,y1+y2=0 then the right statement of
    the following is:
    A) Y5+Y7=0

    B)Y6+Y8=0

    C)2Y2+3Y1=0
    D)Y2+2Y3+Y4=0
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  2. #2
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    Hello, Diligent_Learner!

    y_n is a geometric sequence such that: . y_1+y_2\:=\:0
    then which of the following is correct?

    A)\;\;y_5\;+\;y_7 \:=\:0\qquad B)\;\;y_6\;+\;y_8\:=\:0 \qquad C)\;\;2y_2\;+\;3y_1\:=\:0 \qquad D)\;\;y_2\;+\;2y_3\;+\;y_4\:=\:0

    A geometric series has the form: . a,\:ar,\;ar^2,\;ar^3,\:\hdots\quad \text{ where }a \neq 0

    Since y_1+y_2 \:=\:0, we have: . a + ar \:=\:0 \quad\Rightarrow\quad a(1+r) \:=\:0

    . . Since a \neq 0, then r+1 \:=\:0 \quad\Rightarrow\quad r = \text{-}1


    Hence, the sequence is: . a,\:\text{-}a,\:a,\:\text{-}a,\:a,\: \hdots

    . . That is: . y_n \;=\;\bigg\{ \begin{array}{cc}a & \text{for odd }n \\ \text{-}a & \text{for even }n \end{array}


    A)\;\;y_5+y_7 \:=\:a + a \:=\:2a . . . false

    B)\;\;y_6+y_8 \:=\:(\text{-}a) + (\text{-}a) \:=\:-2a . . . false

    C)\;\;2y_2 + 3y_1 \:=\:2(\text{-}a) + 3(a) \:=\:a . . . false

    D)\;\;y_2 +2y_3 + y_4 \:=\:(\text{-}a) + 2(a) + (\text{-}a) \:=\:0 . . . True!

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  3. #3
    Junior Member
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    Quote Originally Posted by Soroban View Post
    Hello, Diligent_Learner!


    A geometric series has the form: . a,\:ar,\;ar^2,\;ar^3,\:\hdots\quad \text{ where }a \neq 0

    Since y_1+y_2 \:=\:0, we have: . a + ar \:=\:0 \quad\Rightarrow\quad a(1+r) \:=\:0

    . . Since a \neq 0, then r+1 \:=\:0 \quad\Rightarrow\quad r = \text{-}1


    Hence, the sequence is: . a,\:\text{-}a,\:a,\:\text{-}a,\:a,\: \hdots

    . . That is: . y_n \;=\;\bigg\{ \begin{array}{cc}a & \text{for odd }n \\ \text{-}a & \text{for even }n \end{array}


    A)\;\;y_5+y_7 \:=\:a + a \:=\:2a . . . false

    \text{-}a) + (\text{-}a) \:=\:-2a" alt="B)\;\;y_6+y_8 \:=\\text{-}a) + (\text{-}a) \:=\:-2a" /> . . . false

    C)\;\;2y_2 + 3y_1 \:=\:2(\text{-}a) + 3(a) \:=\:a . . . false

    \text{-}a) + 2(a) + (\text{-}a) \:=\:0" alt="D)\;\;y_2 +2y_3 + y_4 \:=\\text{-}a) + 2(a) + (\text{-}a) \:=\:0" /> . . . True!

    Thank you very much ..really I understand the question
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