Multiple Choice Question (MCQ)

If \{a_n\} is a geometric sequence in which a_4\cdotp a_7=-512 , a_3+a_8=124, and its common ratio q\in Z, then a_{10}= is

  1. ×

    256

  2. ×

    -256

  3. 512

  4. ×

    -512

Collected in the board: Geometric sequence

Steven Zheng posted 1 month ago


Answer

  1. Since \{a_n\} is a geometric sequence

    a_4\cdotp a_7=a_3\cdotp a_8=-512

    and

    a_3+a_8=124

    Therefore, a_3, a_8 are two real roots of the quadratic equation

    x^2-124x-512=0

    Solve the function

    a_3= -4,a_8=128 or a_3=128, a_8= -4

    q^5=a_8/a_3= -32 or -1/32

    q = -2 or q = -1/2 (cancel as q \in Z)

    a_{10}=a_3\cdotp q^7=(-4)\cdotp (-2)^7=512

    C is the choice



Steven Zheng posted 1 month ago

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