Question

Write the sum using summation notation, assuming the suggested pattern continues. 2 - 8 + 32 - 128 + ...

Answer 1

This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
  an = a1*r^(n-1)

The sum is the sum of such terms.
$sum=\sum\limits_{n=1}^{\infty}{2(-4)^{(n-1)}}$