JAMIA 2021 — Mathematics PYQ

Let the first term of the Arithmetic Progression be $a$ and the common difference be $d$. The $n^{\text{th}}$ term is given by:

2. Set Up the Given Equations

From the problem, the $p^{\text{th}}$ term is $q$:

The $(p+q{)}^{\text{th}}$ term is $0$:

3. Solve for the Common Difference ($d$)

Subtract equation (1) from equation (2):

4. Solve for the First Term ($a$)

Substitute $d=-1$ into equation (1):

5. Find the $q^{\text{th}}$ term ($T_q$)

Using the formula for the $q^{\text{th}}$ term:

Substitute the values of $a$ and $d$:

Final Result

The $q^{\text{th}}$ term is $p$.