The general term of a sequence is given by $T_n = \frac{n(n+1)}{2}$. We need to find the value of $T_6 - T_2$.

1. Problem Description

The general term of a sequence is given by $T_n = \frac{n(n+1)}{2}$. We need to find the value of $T_6 - T_2$.

2. Solution Steps

First, we find the value of $T_6$ by substituting $n = 6$ into the formula:

$T_6 = \frac{6(6+1)}{2} = \frac{6(7)}{2} = \frac{42}{2} = 21$

Next, we find the value of $T_2$ by substituting $n = 2$ into the formula:

$T_2 = \frac{2(2+1)}{2} = \frac{2(3)}{2} = \frac{6}{2} = 3$

Finally, we find the difference between $T_6$ and $T_2$:

$T_6 - T_2 = 21 - 3 = 18$

3. Final Answer

The value of $T_6 - T_2$ is 18.