1.1 Consider the pattern: 10; 7; 4; 1; ... 1.1.1 Determine the formula $T_n$, the general term of the sequence. 1. The sequence decreases by 3 each time: $10, 7, 4, 1, ...$ 2. This is an arithmetic sequence with first term $a = 10$ and common difference $d = -3$. 3. The formula for the $n$th term of an arithmetic sequence is: $$T_n = a + (n-1)d$$ 4. Substitute $a = 10$ and $d = -3$: $$T_n = 10 + (n-1)(-3)$$ 5. Simplify: $$T_n = 10 - 3(n-1) = 10 - 3n + 3 = 13 - 3n$$ 1.1.2 Which term in the sequence is equal to $-113$? 1. Set $T_n = -113$: $$13 - 3n = -113$$ 2. Solve for $n$: $$-3n = -113 - 13$$ $$-3n = -126$$ $$\cancel{-3}n = \cancel{-126} / -3$$ $$n = 42$$ Answer: The 42nd term is $-113$.