અહીં $2, 5, 8, ..$ ના $2n$ પદનો સરવાળો

${S_{2n}}\,\, = \,\,\frac{{2n}}{2}\,\,\left[ {2\,(2)\, + \,(2n\, – \,1)\,3} \right]$

$ = \,\,n\,\,(4\, + \,6n\, – \,3) = \,\,n\,(6n\, + \,1)\,\,\,\,….\,(1)$

અને $57, 59, 61, …..$ ના $n$ પદનો સરવાળો

$S{'_n}\,\, = \,\,\frac{n}{2}\,\left[ {2\,(57)\, + \,(n\, – \,1)\,2\,} \right]\,\, = \,\,n\,(n\, + \,56)\,\,…\,(2)$

અહીં  $S_{2n} = S'_n$ આપેલ છે.

$\therefore \,\,n\,(6n\, + \,1)\,\, = \,\,n\,\,(n\, + \,56)\,\,\,$

$\,\therefore \,\,\,\,6n\, + \,1\,\, = \,\,n\, + \,56\,\,$

$\,\therefore \,\,5n\,\, = \,\,55\,\,\,\therefore \,\,n\,\, = \,\,11$