Geometric Sequence

Question

Consider the following geometric sequence

-5,10,-20,40...

If the explicit formula for the sequence above is in the form a_n=b(c)^n-1, determine the value of b and c

Answer 1

Apparently 

 

a₁=b(c)⁰ = b*1 = -5, or b = -5

a₂=-5(c)¹ = 10, or c = -2

Answer 2

a_n = (2a_n-1)(-1)^n-1

 

So what is b and c?

Answer 3

b = -5    r = -2  because the first term is -5 (when n=1) and you can see the sign changes from term to term and the absolute values double from term to term.