text: first 6 terms of geometric series? 27-9+3-1+1/3-1/9+1/27  i need to know the steps using an equation, i found it by adding up but need to know it the other way, any help is great... thanks hey guys, the question asks for a series, not a sequence.  the formula for any geometric series for n terms is given by:  a * [1-r^(n+1)] / (1-r)  where a is the first term, r is the ratio, and n is the # of terms  for example, in your case, for 6 terms,  you'll have s(6) = 27 * (1-(-1/3)^6)/(1-(-1/3))  for 5 terms:   s(5) = 27 * (1-(-1/3)^5)/(1-(-1/3))  and so on ...