What is S7 for 6 - 24 + 96 - 384 + ... ?

6 - 34 + 96 - 384 + ...

a 1 = 6, a 2 = a 1 * ( - 4), a 3 = a 2 * ( - 4), a 4 = a 3 * ( - 4) ...

a 5 = - 384 * ( - 4) = 1,536

a 6 = 1536 * ( - 4) = - 6,144

a 7 = - 6,144 * ( - 4) = 24,576

This is a sum of a geometric sequence:

S 7 = 6 - 24 + 96 - 384 + 1,536 - 6,144 + 24,576 = 19,662

Another way to solve this:

S 7 = a 1 * (r^n - 1) / (r - 1) = 6 * (( - 4) ^7 - 1) / ( - 4 - 1) =

= 6 * (-16,385) / (-5) = 19,662