Question 1150467
T[n] = 10/3 - n/3.


T[1] = 10/3 - 1/3 = 9/3


T[2] = 10/3 - 2/3 = 8/3


T[3] = 10/3 - 3/3 = 7/3


T[n+1] = 10/3 - (n+1)/3


T[n+1] - T[n] = 10/3 - (n+1)/3 - (10/3 - n/3)
simplify this to get:
T[n+1] - T[n] = 10/3 - (n+1)/3 - 10/3 + n/3
combine like terms to get:
T[n+1] - T[n] = -(n+1)/3 + n/3 = (-n - 1 + n) / 3 = -1/3


for example:


T3 = 10/3 - 3/3 = 7/3
T2 = 10/3 - 2/3 = 8/3


if you let T[n] = T[2] and, if you let T[n+1] = T[3], then you get:
T[n+1] - T[n] = T[3] - T[2] = (10/3 - 3/3) - (10/3 - 2/3) = 7/3 - 8/3 = -1/3.


this is correct according to the formula, as far as i can tell.


further, if you look at T[1] and T[2] and T[3], you will see that each succeeding value is 1/3 less than the preceding value by 1/3.