Question

What is the sum of the first five terms of the geometric series 1 − 3 + 9 −...

Answer 1

$\bf 1~~,~~\stackrel{-3\cdot 1}{-3}~~,~~\stackrel{-3\cdot -3}{9}~~,~~\stackrel{-3\cdot 9}{-27}~~,~~\stackrel{-3\cdot -27}{81}$

notice, the "common ratio" is -3, thus their sum is just

1 + (-3) + 9 + (-27) + 81.