Question

Write the sum using summation notation, assuming the suggested pattern continues. 1 - 3 + 9 - 27 + ...

Answer 1

Σ-3^(n-1)  for n=[1,n]

Angie above is correct though as there is no sum for this as an infinite series as r^2>1.

The only time infinite series have a sum is if r^2<1, and that sum is just s=a/(1-r)

Answer 2

There is no sum for this geometric series. it diverges rather than converges due to the absolute value of the common ratio (r), which is -3, being 3. for a geometric series to have a sum (to converge), the absolute value of r must be less than 1. 
(you find r by dividing a2/a1, a3/a2, etc.)
hope this helps