Question

write an explicit formula for the sequence: 1/2, -1/4, 1/8, -1/6.

i know that the ratio is -0.5 but im confused on how to write this into a explicit formula.

Answer 1

This is a geometric sequence because there is a common ration.  Which means that each term is a constant multiple of the previous term...in this case:

r=(-1/4)/(1/2)=(1/8)/(-1/4)=-1/2

Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number...in this case:

a(n)=(1/2)(-1/2)^(n-1)