Respuesta :
Answer:
[tex]-\frac{2}{5}[/tex]
Step-by-step explanation:
The geometric progression given is:
-6250, 1250, -250...
The first term (a) is -6250, and the common ratio (r) can be gotten by dividing the second term by the first term:
r = 1250/-6250 = [tex]-\frac{1}{5}[/tex]
A geometric progression is generally given as:
[tex]a_n = ar^{n - 1}[/tex]
where [tex]a_n[/tex] = nth term
The 7th term of the progression above is therefore:
[tex]a_7 = -6250 * (-\frac{1}{5} )^6\\\\a_7 = -\frac{2}{5}[/tex]
The 7th term of the geometric progression is;
a_7 = -2/5
The formula for the nth term of a geometric progression is;
a_n = ar^(n - 1)
Where;
a is first term
r is common ratio
n is the position of the term in the series
We are given the series;
-6250, 1250, -250...
Thus;
First term; a = -6250
Common ratio; r = 1250/-6250
r = -1/5
Thus;
a_7 = -6250(-1/5)^(7 - 1)
a_7 = -2/5
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