Correct Answer - Option 4 : Q
Concept:
Sum of n AP terms = \({{\rm{S}}_{\rm{n}}} = \frac{{\rm{n}}}{2}\left[ {2{\rm{a}} + \left( {{\rm{n}} - 1} \right){\rm{d}}} \right]\)
Where a is the first term of AP and d is the difference between two consecutive terms of AP.
Calculation:
Given that,
\(S_n = nP + \frac{n(n-1)}{2}Q\)
\(\Rightarrow \ S_n = \frac{n}{2}[2P + (n-1)Q]\) ----(1)
We know that the sum of the nth term of AP is
\({{\rm{S}}_{\rm{n}}} = \frac{{\rm{n}}}{2}\left[ {2{\rm{a}} + \left( {{\rm{n}} - 1} \right){\rm{d}}} \right]\) ----(2)
From equation (1) and (2)
a = P, d = Q
Hence, the first term of the A.P is P and the common difference is Q.