${S_1} = \frac{1}{2}a{(P - 1)^2}$ and ${S_2} = \frac{1}{2}a\;{P^2}$       $[As\;u = 0$]

From ${S_n} = u + \frac{a}{2}(2n - 1)$

${S_{{{({P^2} - P + 1)}^{th}}}} = \frac{a}{2}\left[ {2({P^2} - P + 1) - 1} \right]$

$ = \frac{a}{2}\left[ {2{P^2} - 2P + 1} \right]$

It is clear that ${S_{{{({P^2} - P + 1)}^{th}}}} = {S_1} + {S_2}$