im pretty sure im correct, just want to make sure.

You take one-fourth and change the sign. 

This is  a geometric series

The sum, S,  is given by

S  =   frst term *   [  1  -  r^n ]  / [ 1 - r ]

Where  r  = the common ratio  =  -(1/4)     and  n  = 6

So we have

S =  48  [  1 - (-1/4)^6 ] / [ 1 - (-1/4) ]   =   48 [ 1 -  1/4096 ] / [ 5/4]  =

48 ( 4/5) [ 4096 - 1 ] / 4096  =

[(48 ( 4)) / 4096] *  ( 4095 / 5) =

[3/64]  * [ 819 ] =

2457 / 64