Final answer:
The first three terms of the sequence defined by Tn = 4n³ - 6n² + Tn-1 with T0 = 2 are calculated as T1=0, T2=8, and T3=62, corresponding to option A.
Step-by-step explanation:
The question asks to calculate the first three terms of the sequence defined by the recurrence relation Tn = 4n³ - 6n² + Tn-1 with the initial condition T0 = 2.
To find T1, plug n=1 into the equation:
- T1 = 4(1)³ - 6(1)² + T0
- T1 = 4 - 6 + 2
- T1 = 0
Now to find T2, substitute n=2:
- T2 = 4(2)³ - 6(2)² + T1
- T2 = 32 - 24 + 0
- T2 = 8
Finally, we calculate T3:
- T3 = 4(3)³ - 6(3)² + T2
- T3 = 108 - 54 + 8
- T3 = 62
Thus, the correct answer is T1=0, T2=8, T3=62, which corresponds to option A).