1. **Problem:** In an arithmetic progression (AP), the first term $a_1=2$ and the sum of the 1st and 6th terms is $16 \frac{1}{2} = 16.5$. Find the 4th term $a_4$. 2. **Formula and rules:** The $n$th term of an AP is given by $$a_n = a_1 + (n-1)d$$ where $d$ is the common difference. 3. **Step 1:** Write the sum of the 1st and 6th terms: $$a_1 + a_6 = 16.5$$ Substitute $a_1=2$ and $a_6 = a_1 + 5d = 2 + 5d$: $$2 + (2 + 5d) = 16.5$$ 4. **Step 2:** Simplify and solve for $d$: $$4 + 5d = 16.5$$ $$5d = 16.5 - 4 = 12.5$$ $$d = \frac{12.5}{5} = 2.5$$ 5. **Step 3:** Find the 4th term: $$a_4 = a_1 + 3d = 2 + 3 \times 2.5 = 2 + 7.5 = 9.5$$ 6. **Answer:** The 4th term is $9.5$, which corresponds to option (b) 9 1/2. The underlined answer (b) 9 1/2 is correct.