oscar8338
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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.

Verified Answer :

LammettHash

\(a_5=ra_4=r^2a_3=r^3a_2\)
\(2304=-36r^3\implies r=-4\)

Since \(a_2=ra_1\implies -36=-4a_1\implies a_1=9\), the sequence takes the form

\(a_n=(-4)^{n-1}a_1=9(-4)^{n-1}\)

Answer:

\(a_n=9*4^n^-^1\)

Step-by-step explanation:

Substitute the value of n for the nth term

\(a_2=9*4^(^2^)^-^1\)

Subtract 1 from 2

\(a_2=9*4\)

Multiply 9 by 4

\(a_2=36\)

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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