Give the first three terms of the sequence of 1.Tn+1=Tn+n
Tn-1,Tn-2,Tn-3
T1
T2 = T1+1
T3 = T2+2 = T1+3
...
Tn = T1 + n(n+1)/2
To find the first three terms of the sequence defined by the formula Tn+1 = Tn + n, we can start by determining the value of T1.
Given the formula Tn+1 = Tn + n, let's substitute n = 1 to find T2:
T2 = T1 + 1
Next, we substitute n = 2 to find T3:
T3 = T2 + 2
To continue, we need the value of T1. Since we don't have any specific information, we can choose an arbitrary value for T1. Let's assume T1 = 0.
Substituting T1 = 0, we can calculate the first three terms:
T1 = 0
T2 = T1 + 1 = 0 + 1 = 1
T3 = T2 + 2 = 1 + 2 = 3
Therefore, the first three terms of the sequence are 0, 1, and 3.