` a=2,d=8 ` और ` S_n =90 `दिया है| n और a ज्ञात कीजिए| एक `A.P.` में,

Explanation

` " "a=2 ,d=8`
तथा `" " S_n =90`
` rArr " " (n)/(2) [2a +(n-1) *d] =90`
` rArr " " (n)/(2) [2xx2 +(n-1) *8] =90`
`rArr " " n(2n -1 ) =(90xx2)/(4)`
`rArr " " 2n^(2) -n =45`
` rArr " " 2n^(2)-n -45 =0`
` rArr" " 2n^(2) -10n +9n -45 =0`
` rArr 2n (n-5) +9 (n-5) =0`
` rArr " " (n-5)(2n+ 9) =0`
` rArr " " n-5=0 ` या ` 2n +9 =0`
` rArr" " n=5` या ` " " n=-(9)/(2)`
परन्तु `" " n=-(9)/(2)` सम्भव नहीं है|
` therefore " " n=5`
अब, ` " " a_n =a +(n-1) d`
`rArr " " a_5 =2 + (5-1) xx8=2 +32 =34`
` therefore " " n=5` तथा ` a_n =34`