Question

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

Answer 1

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

Answer 2

The answer is 19,662