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=(10)/(-5)=-2`