EXPLANATION
A geometric sequence has a constant ratio r and it's defined by:
[tex]a_n=a_0\cdot r^{n-1}[/tex]Check wheter the ratio is constant:
-2.5, 5, -10, 20,...
Compute the ratio of all the adjacent terms:
[tex]r=\frac{a_{n+1}}{a_n}[/tex]5/-2.5= -2 , -10/5 = -2, 20/-10=-2
The ratio of all the adjacent terms is the same and equal to:
r= -2
The first element of this sequence is:
[tex]a_1=-2.5[/tex][tex]a_n=a_1\cdot r^{n-1}[/tex]So, the next term of the sequence is:
[tex]a_5=-2.5\cdot-2^{5-1}[/tex]Simplifying:
[tex]a_5=-2.5\cdot16[/tex]So, the next term is a_5 = -40
