Respuesta :

Stephen46

Answer:

[tex]d(n) = { - 7}^{n - 1} [/tex]

Step-by-step explanation:

Since the sequence above is a geometric sequence

For an nth term in a geometric sequence

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

where

a is the first term

r is the common ratio

n is the nth term

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

That's

[tex]r = \frac{ - 7}{ - 1} = 7 \: \: \: \: or \\ r = \frac{ - 49}{ - 7} = 7 \: \: \: or \\ r = \frac{ - 343}{ - 49} = 7[/tex]

So the common ratio / r = 7

the first term is - 1

Substitute the values into the above formula

[tex]d(n) = - 1( {7})^{n - 1} \\ [/tex]

We have the final answer as

[tex]d(n) = { - 7}^{n - 1} [/tex]

Hope this helps you

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