Question

Consider the following geometric sequence.

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

In the explicit formula for the sequence above is expressed in the form an=b*c^n-1, determine the values of b and c.

Answer 1

If you would like to know the values of b and c, you can calculate this using the following steps:

an = b * c^(n-1)
a1 = - 5
a1 = b * c^(1-1) = b * c^0 = b * 1 = b
_______________
b = - 5

a2 = 10
a2 = b * c^(2-1) = (-5) * c ^1 = (-5) * c
_______________
10 = (-5) * c
c = - 2

an = b * c^(n-1) ... an = (-5) * (-2)^(n-1)
a3 = (-5) * (-2)^(n-1) = (-5) * (-2)^(3-1) = (-5) * (-2)^2 = (-5) * 4 = -20
a4 = (-5) * (-2)^(n-1) = (-5) * (-2)^(4-1) = (-5) * (-2)^3 = (-5) * (-8) = 40

The correct result would be: b = -5 and c = -2.