Mathematics

Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.

2 Answer

  • [tex]a_5=ra_4=r^2a_3=r^3a_2[/tex]
    [tex]2304=-36r^3\implies r=-4[/tex]

    Since [tex]a_2=ra_1\implies -36=-4a_1\implies a_1=9[/tex], the sequence takes the form

    [tex]a_n=(-4)^{n-1}a_1=9(-4)^{n-1}[/tex]
  • Answer:

    [tex]a_n=9*4^n^-^1[/tex]

    Step-by-step explanation:

    Substitute the value of n for the nth term

    [tex]a_2=9*4^(^2^)^-^1[/tex]

    Subtract 1 from 2

    [tex]a_2=9*4[/tex]

    Multiply 9 by 4

    [tex]a_2=36[/tex]

    This is the only option from the choices that has a second term of 36 so it is the only option that satisfies the requirements.

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