9 + 17 + 25 + ……. + a_{n} = 636

a = 9, d = 17 – 9 = 8, S_{n}= 636, n =?

n(8n + 10) = 636 × 2

8n^{2} + 10n = 1272

8n^{2}+ 10n – 1272 = 0

4n^{2} + 5n – 636 = 0

4n^{2}+ 5n – 48n – 636 = 0

n(4n + 5) – 12(4n + 5) = 0

(4n + 5) (n – 12) = 0

if n – 12 = 0 then, n = 12

∴ n = 12.