1. The problem asks us to find the first three terms of the sequence defined by the formula $T(n) = 5n - 7$. 2. The formula for the $n^{th}$ term of the sequence is given as: $$T(n) = 5n - 7$$ This means to find the term at position $n$, multiply $n$ by 5 and then subtract 7. 3. Calculate the first term ($n=1$): $$T(1) = 5(1) - 7 = 5 - 7 = -2$$ 4. Calculate the second term ($n=2$): $$T(2) = 5(2) - 7 = 10 - 7 = 3$$ 5. Calculate the third term ($n=3$): $$T(3) = 5(3) - 7 = 15 - 7 = 8$$ 6. Therefore, the first three terms of the sequence are: $$-2, 3, 8$$