If p^ th term of an AP is k , then what is the sum of p^ th term,...

Let the first term of the AP be $a$ and the common difference be $d$.

The $p^{\text{th}}$ term is given by $T_p = a + (p-1)d = k$.

The $(p+q)^{\text{th}}$ term is $T_{p+q} = a + (p+q-1)d$.

The $(p-q)^{\text{th}}$ term is $T_{p-q} = a + (p-q-1)d$.

The required sum is $T_p + T_{p+q} + T_{p-q}$.

Substituting the values, we get:

$[a + (p-1)d] + [a + (p+q-1)d] + [a + (p-q-1)d]$

$= 3a + d[(p-1) + (p+q-1) + (p-q-1)]$

$= 3a + d(3p - 3)$

$= 3[a + (p-1)d]$

Since $a + (p-1)d = k$, the sum is $3k$.

Answer: $3k$