Question

Consider the following geometric sequence.

-5,10,-20,40

If 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

b = -5, c = -2

Explanation:

The explicid formula of a geometric sequence:

`a_n=a_1\cdot r^(n-1)`

We have

`a_1=-5,\ a_2=10,\ a_3=-20,\ a_4=40\\\\r=(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)\to r=(10)/(-5)=-2`

Substitute:

`a_n=-5\cdot(-2)^(n-1)\\\\-5\cdot(-2)^(n-1)=b\cdot c^(n-1)\Rightarrow b=-5\ \text{and}\ c=-2`