1. The first problem asks for the formula to find the nth term of the sequence defined by $f(x) = 3x + 4$ for $x = 1, 2, 3, 4, \ldots$. 2. The general form for the nth term of a sequence is often written as $f(n)$ where $n$ is the term number. 3. Since the sequence is given by $f(x) = 3x + 4$, replacing $x$ with $n$ gives the nth term as: $$f(n) = 3n + 4$$ 4. Therefore, the correct choice is C: $f(n) = 3n + 4$. --- 5. The second problem is a geometric progression: $6, 18, 54, \_, 486$. 6. In a geometric progression, each term is found by multiplying the previous term by a constant ratio $r$. 7. To find $r$, divide the second term by the first term: $$r = \frac{18}{6} = 3$$ 8. Verify the ratio with the third term: $$\frac{54}{18} = 3$$ 9. The missing fourth term is the third term multiplied by $r$: $$\text{4th term} = 54 \times 3 = 162$$ 10. Check the fifth term: $$\text{5th term} = 162 \times 3 = 486$$ 11. The missing number in the progression is 162, so the correct answer is C. Final answers: - For the nth term formula: C - For the missing number in the geometric progression: C