1. **Problem statement:** We have two pairs of sequences. For each pair, the second sequence is formed from the first by adding, subtracting, or multiplying by a number. We need to find the nth term formula for the second sequence. 2. **Part a:** - First sequence: 7, 10, 13, 16, ... with nth term $3n + 4$ - Second sequence: 8, 11, 14, 17, ... 3. **Step 1:** Compare the sequences term-by-term: - 1st terms: 7 and 8 - 2nd terms: 10 and 11 - 3rd terms: 13 and 14 - 4th terms: 16 and 17 4. **Step 2:** Notice the second sequence is always 1 more than the first sequence. 5. **Step 3:** Since the first sequence nth term is $3n + 4$, the second sequence nth term is: $$3n + 4 + 1 = 3n + 5$$ 6. **Answer for a:** The nth term of the second sequence is $3n + 5$. 7. **Part b:** - First sequence: 2, 5, 8, 11, ... with nth term $3n - 1$ - Second sequence: 4, 10, 16, 22, ... 8. **Step 1:** Compare the sequences term-by-term: - 1st terms: 2 and 4 - 2nd terms: 5 and 10 - 3rd terms: 8 and 16 - 4th terms: 11 and 22 9. **Step 2:** Check if the second sequence is a multiple of the first: - $4 = 2 imes 2$ - $10 = 5 imes 2$ - $16 = 8 imes 2$ - $22 = 11 imes 2$ 10. **Step 3:** The second sequence is the first sequence multiplied by 2. 11. **Step 4:** Since the first sequence nth term is $3n - 1$, the second sequence nth term is: $$2(3n - 1) = 6n - 2$$ 12. **Answer for b:** The nth term of the second sequence is $6n - 2$. **Final answers:** - a) $3n + 5$ - b) $6n - 2$