Answer:
b = -5, c = -2
Step-by-step explanation:
The explicid formula of a geometric sequence:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
We have
[tex]a_1=-5,\ a_2=10,\ a_3=-20,\ a_4=40\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\to r=\dfrac{10}{-5}=-2[/tex]
Substitute:
[tex]a_n=-5\cdot(-2)^{n-1}\\\\-5\cdot(-2)^{n-1}=b\cdot c^{n-1}\Rightarrow b=-5\ \text{and}\ c=-2[/tex]
