Mathematics
Carole572
16

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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(1) Answers
jackie1977

[latex]a_5=ra_4=r^2a_3=r^3a_2[/latex] [latex]2304=-36r^3\implies r=-4[/latex] Since [latex]a_2=ra_1\implies -36=-4a_1\implies a_1=9[/latex], the sequence takes the form [latex]a_n=(-4)^{n-1}a_1=9(-4)^{n-1}[/latex]

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