` A.P. 9, 17,25 ,.......` के कितने पदों का योग 636 होगा?

Explanation

` 9,17,25.......`
यहाँ ` a= 9, d=17-9=25 -17 =8`
माना ` " " S_n =636`
` rArr " " (n)/(2) [2 (9) +(n-1) 8]=636`
` rArr " " (n)/(2) (18+8n -8) =636`
` rArr " " n( 4n +5 ) =636`
` rArr " " 4n^(2) +5n -636 =0`
` rArr " " n( 4n +5 ) =636`
` rArr " " 4n^(2) +5n -636 =0`
` rArr " " ( 4n + 53 ) (n-12)=0`
` " " n= (53)/(4) ` या ` " " n=12`
` " " n= -(53)/( 4) ` सम्भव नहीं है|
` therefore " " n=12 `