1. **State the problem:** We are given a sequence starting with the first term unknown, and the term-to-term rule is "Multiply by a number then subtract 2". The sequence provided is 7, 12, 22, 42, ... 2. **Identify the term-to-term rule:** Let the multiplier be $m$. The rule is: $$a_{n+1} = m \times a_n - 2$$ 3. **Use the given terms to find $m$:** From the first two terms: $$12 = m \times 7 - 2$$ Add 2 to both sides: $$12 + 2 = m \times 7$$ $$14 = 7m$$ Divide both sides by 7: $$\frac{14}{\cancel{7}} = \cancel{7}m$$ $$2 = m$$ 4. **Verify the rule with $m=2$ for the next terms:** Check if $22 = 2 \times 12 - 2$: $$2 \times 12 - 2 = 24 - 2 = 22$$ Correct. Check if $42 = 2 \times 22 - 2$: $$2 \times 22 - 2 = 44 - 2 = 42$$ Correct. 5. **Find the first term:** The first term is given as 7. **Final answer:** - First term: $7$ - Term-to-term rule: Multiply by $2$ then subtract $2$