1. **Problem statement:** Given the arithmetic progression (AP) term formula $T_n = 2 - 3n$, find: i. The first term $T_1$. ii. The sequence of terms. iii. Write the general term $T_n$ up to a certain term. iv. Find the 11th term $T_{11}$. 2. **Formula and rules:** The $n$th term of an AP is given by $T_n = a + (n-1)d$ where $a$ is the first term and $d$ is the common difference. 3. **Step i: Find the first term $T_1$** Substitute $n=1$ into $T_n = 2 - 3n$: $$T_1 = 2 - 3(1) = 2 - 3 = -1$$ 4. **Step ii: Write the sequence of terms** Calculate first few terms: $$T_1 = -1$$ $$T_2 = 2 - 3(2) = 2 - 6 = -4$$ $$T_3 = 2 - 3(3) = 2 - 9 = -7$$ $$T_4 = 2 - 3(4) = 2 - 12 = -10$$ So the sequence is: $-1, -4, -7, -10, \ldots$ 5. **Step iii: Write the general term $T_n$ up to a certain term** The formula is already given as: $$T_n = 2 - 3n$$ This can be rewritten as: $$T_n = -1 - 3(n-1)$$ Here, $a = -1$ and $d = -3$. 6. **Step iv: Find the 11th term $T_{11}$** Substitute $n=11$ into $T_n = 2 - 3n$: $$T_{11} = 2 - 3(11) = 2 - 33 = -31$$ **Final answers:** - First term $T_1 = -1$ - Sequence starts as $-1, -4, -7, -10, \ldots$ - General term $T_n = 2 - 3n$ - 11th term $T_{11} = -31$