T_2 = mixed fraction 6 1/2 and T_10 = mixed fraction 18 1/2, determine the common difference.
To find the common difference, we need to find the difference between two consecutive terms.
To find the difference between T_2 and T_1, we subtract T_1 from T_2:
T_2 - T_1 = (6 1/2) - (18 1/2)
To subtract mixed fractions, we need to convert them to improper fractions.
6 1/2 = (6*2 + 1)/2 = 13/2
18 1/2 = (18*2 + 1)/2 = 37/2
So, T_2 - T_1 = 13/2 - 37/2 = -24/2 = -12
Therefore, the common difference is -12.