Multiple Choice Question (MCQ)

If \{a_n\} is a geometric sequence with all terms greater than 0, and common ration q\ne 1, then

  1. a_1+a_8 > a_4+a_5

  2. ×

    a_1+a_8 < a_4+a_5

  3. ×

    a_1+a_8 = a_4+a_5

  4. ×

    It's uncertain

Collected in the board: Geometric sequence

Steven Zheng Steven Zheng posted 3 weeks ago


Answer

  1. a_8 = a_1q^7

    a_4 = a_1q^3

    a_5 = a_1q^4

    a_1+a_8 = a_1(1+q^7)

    a_4+a_5 = a_1(q^3+q^4)

    a_1+a_8-(a_4+a_5 ) = a_1(1+q^7-q^3-q^4)

    =a_1(1-q^3)(1-q^4)

    =a_1(1+q^2)(1-q)^2(1+q)(q^2+q+1)>0


    Therefore, a_1+a_8 > a_4+a_5

Steven Zheng Steven Zheng posted 3 weeks ago

Scroll to Top