Answer:
The explicit formula for the geometric sequence is [tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex].
Step-by-step explanation:
By definition of geometric sequence, we should use the following expression:
[tex]c(n) = c_{1}\cdot r^{n-1}[/tex], [tex]n \ge 1[/tex] (1)
Where:
[tex]c_{1}[/tex] - First term.
[tex]r[/tex] - Geometric rate.
[tex]n[/tex] - Position of the element within the series.
If we know that [tex]c_{1} = -40[/tex] and [tex]r = \frac{1}{2}[/tex], then the explicit formula for the geometric sequence is:
[tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex]
The explicit formula for the geometric sequence is [tex]c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}[/tex].
