oscar8338 oscar8338

01-02-2017
Mathematics

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

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LammettHash LammettHash

01-02-2017

[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]

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