The sum is 7 2/9.
The first 3 numbers of the sequence can be written as
3/1, 6/3, 12/9
Each numerator is being doubled and each denominator is being tripled; this means the fourth term would be 24/27.
Now we can simplify these in order to add them:
3/1 = 3
6/3 = 2
12/9 = 1 1/3
24/27 = 8/9
Adding the whole numbers, we have 6; now we must add 1/3 + 8/9. The LCD for these two is 9:
3/9 + 8/9 = 11/9
We have 6 11/9; simplifying this we have 7 2/9.
