contestada

What is the nth term of the geometric sequence that has a common ratio of 6 and 24 as its third term? A. ` ` ` ` `a_(n)=24(6)^(n-1)` B. `a_n=2/3(6)^(n-1)` C. `a_(n)=24(6)^n` D. `a_(n)=3/2(6)^(n-1)`

Respuesta :

lilblakey69

Answer:

B. `a_n=2/3(6)^(n-1)`

Answer:

Option B. is the answer.

Step-by-step explanation:

Explicit formula of a geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex].

As given in the question

common ratio r = 6

and [tex]a_{3}=6[/tex]

[tex]a_{3}=a(6)^{3-1}[/tex]

[tex]24=a(6)^{2}[/tex]

[tex]a=\frac{24}{36}[/tex]

[tex]a=\frac{2}{3}[/tex]

Now we put this values in the explicit formula to get the nth term of the sequence.

[tex]a_{n}=\frac{2}{3}(6)^{n-1}[/tex]

Option B is the answer.

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