Respuesta :

Stephen46

Answer:

The answer is

[tex] \frac{2187}{8} [/tex]

Step-by-step explanation:

The sequence above is a geometric sequence

For an nth term in a geometric sequence

[tex]A(n) = a ({r})^{n - 1} [/tex]

where n is the number of terms

r is the common ratio

a is the first term

From the question

a = - 16

To find the common ratio divide the previous term by the next term

That's

r = 24/-16 = -3/2 or -36/24 = - 3/2

Since we are finding the 8th term

n = 8

Substitute the values into the above formula

That's

[tex]A(8) = - 16 ({ - \frac{3}{2} })^{8 - 1} [/tex]

[tex]A(8) = - 16 ({ - \frac{3}{2} })^{7} [/tex]

[tex]A(8) = - 16( - \frac{2187}{128} )[/tex]

We have the final answer as

[tex]A(8) = \frac{2187}{8} [/tex]

Hope this helps you

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