Respuesta :

sqdancefan
The n-th term a[n] is given by
.. a[n] = 4*(-5)^(n -1)
Then
.. a[7] = 4*(-5)^6 = 62,500

The 3rd selection is appropriate.

Answer:  The correct option is (C) 62500.

Step-by-step explanation:  We are given to find the 7-th term of the following geometric sequence :

4,   −20,   100,    .    .     .

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

For the given geometric sequence, we have

first term, a = 4

and common ratio r is given by

[tex]r=\dfrac{-20}{4}=\dfrac{100}{-20}=~~.~~.~~.~~=-5.[/tex]

Therefore, the 7-th term of the given geometric sequence is

[tex]a_7=ar^{7-1}=4\times(-5)^6=4\times 15625=62500.[/tex]

Thus, the required 7-th term is 62500.

Option (C) is CORRECT.

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