The 9^th term of an A.P. is 449 and 449^th term is 9. The term which is equal to zero is

Solution (By Examveda Team)

$$\eqalign{ & {a_n} = a + \left( {n - 1} \right)d \cr & {a_9} = 449 \cr & \,\,\,\,\,\, = a + \left( {9 - 1} \right)d \cr & \,\,\,\,\,\, = a + 8d\,.....\left( 1 \right) \cr & {a_{449}} = 9 \cr & \,\,\,\,\,\,\,\,\, = a + \left( {449 - 1} \right)d \cr & \,\,\,\,\,\,\,\,\, = a + 448d\,.....\left( 2 \right) \cr & {\text{Subtracting}} \cr & 440d = - 440 \cr & \Rightarrow d = \frac{{ - 440}}{{440}} = - 1 \cr & {\text{and}}\,a + 8d = 449 \cr & \Rightarrow a \times 8 \times \left( { - 1} \right) = 449 \cr & \Rightarrow a = 449 + 8 = 457 \cr & \therefore 0 = a + \left( {n - 1} \right)d \cr & \Rightarrow 0 = 457 + \left( {n - 1} \right)\left( { - 1} \right) \cr & \Rightarrow 0 = 457 - n + 1 \cr & \Rightarrow n = 458 \cr & \therefore {458^{{\text{th}}}}\,{\text{term}} = 0 \cr} $$