Question

Consider the following geometric sequence: -5, 10, -20, 40... if the explicit formula for the sequence above is expressed in the form a^n= b (c)^n-1, determine the values of b and c.

Answer 1

When $n=1$, you get the first term in the sequence, and so

$-5=bc^{1-1}=bc^0=b\implies b=-5$

Then for $n=2$, you must have

$10=bc^{2-1}=b(-5)\implies b=\dfrac{10}{-5}=-2$