Answer:
The nth term of the geometric sequence is given by;
[tex]a_n = a_1r^{n-1}[/tex], .....[1] n is the number of terms.
where,
[tex]a_1[/tex] is the first term and r is the common ratio of the terms.
As per the statement:
Given:
[tex]a_1= 625[/tex] and [tex]a_2 = -125[/tex]
Using [1];
[tex]a_2 = a_1 \cdot r[/tex]
Substitute the value of [tex]a_1[/tex] we have;
[tex]-125 = 625 \cdot r[/tex]
Divide both sides by 625 we have;
[tex]-\frac{1}{5} = r[/tex]
or
[tex]r= -\frac{1}{5}[/tex]
We have to find 7th term of the geometric sequence.
For n = 7 we have;
[tex]a_7 = a_1 \cdot r^6[/tex]
Substitute the given values we have;
[tex]a_7 = 625 \cdot (-\frac{1}{5})^6 = \frac{625}{15625} = \frac{1}{25} =0.04[/tex]
therefore, the 7th term of the geometric sequence is, 0.04
