1. **Problem Statement:** Given an arithmetic progression (AP), the $p$th term is $q$, the $q$th term is $p$. We need to find the $(p+q)$th term. 2. **Formula for the $n$th term of an AP:** $$a_n = a + (n-1)d$$ where $a$ is the first term and $d$ is the common difference. 3. **Using the given information:** - The $p$th term is $q$: $$a_p = a + (p-1)d = q$$ - The $q$th term is $p$: $$a_q = a + (q-1)d = p$$ 4. **Set up equations:** $$a + (p-1)d = q$$ $$a + (q-1)d = p$$ 5. **Subtract the second equation from the first:** $$[a + (p-1)d] - [a + (q-1)d] = q - p$$ $$ (p-1)d - (q-1)d = q - p$$ $$ (p - 1 - q + 1)d = q - p$$ $$ (p - q)d = q - p$$ 6. **Simplify:** $$ (p - q)d = q - p = -(p - q)$$ 7. **Divide both sides by $(p - q)$ (assuming $p \neq q$):** $$ d = -1$$ 8. **Find $a$ using one of the equations, say $a + (p-1)d = q$:** $$ a + (p-1)(-1) = q$$ $$ a - (p-1) = q$$ $$ a = q + p - 1$$ 9. **Find the $(p+q)$th term:** $$ a_{p+q} = a + (p+q - 1)d$$ $$ = (q + p - 1) + (p + q - 1)(-1)$$ $$ = (q + p - 1) - (p + q - 1)$$ $$ = 0$$ **Final answer:** The $(p+q)$th term is $0$. Hence, the correct choice is **D. 0**.