The sum of the first 8 items in the geometric sequence:1, 3, 9, 27, ...etc is 3280.
Step-by-step explanation:
The given is,
             sequence: 1,3,9,21,.. etc
Step:1
            The given is based on multiplication of 3 to previous number,
            ( x - previous number, next number = 3 × 
 )
             First term : 1
             Second term : 1 × 3 = 3
            Third term : 3 × 3 = 9
             Fourth term : 9 × 3 =27
             Fifth term : 27 × 3 = 81
             Sixth term : 81 × 3 = 243
             Seventh term : 243 × 3 = 729
             Eighth term : 729 × 3 = 2187
Step:2
             Sum of first 8 terms 
                                               = 3280
             Sum of first 8 terms = 3280
Result:
            The sum of the first 8 items in the geometric sequence:1, 3, 9, 27, ...etc is 3280.