-233;-199;-153;-119 Find the next two terms and Tn

Given sequence: $-233, -199, -153, -119$.
Calculate the first differences:

• $D_1 = -199 - (-233) = -199 + 233 = 34$
• $D_2 = -153 - (-199) = -153 + 199 = 46$
• $D_3 = -119 - (-153) = -119 + 153 = 34$

The first differences are $34, 46, 34$. This indicates an alternating pattern where the differences are $34, 46, 34, 46, \dots$.

Following the pattern, the next difference ($D_4$) will be 46.

The subsequent difference ($D_5$) will be 34.

The next two terms are $\boxed{-73, -39}$.

The sequence of first differences $D_k$ can be expressed as $D_k = A + B(-1)^k$.
Using $D_1 = 34$ and $D_2 = 46$:
For $k=1$: $A - B = 34$
For $k=2$: $A + B = 46$
Adding these equations: $2A = 80 \implies A = 40$.
Subtracting the first from the second: $2B = 12 \implies B = 6$.
So, the formula for the differences is $D_k = 40 + 6(-1)^k$.

The general term $T_n$ is given by $T_n = T_1 + \sum_{k=1}^{n-1} D_k$ for $n > 1$.

The first sum is $40(n-1)$.
The second sum is $6 \times \left( \frac{(-1)^{n-1}-1}{2} \right)$.

The formula for $T_n$ is $\boxed{T_n = 40n - 276 + 3(-1)^{n-1}}$.