Examveda

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is :

A. 13

B. 9

C. 21

D. 17

\eqalign{ & \therefore a - d + a + a + d = 51 \cr & \Rightarrow 3a + 51 \cr & \therefore a = \frac{{51}}{3} = 17 \cr}
\eqalign{ & = \left( {a - d} \right)\left( {a + d} \right) = 273 \cr & \Rightarrow {a^2} - {d^2} = 273 \cr & \Rightarrow {\left( {17} \right)^2} - {d^2} = 273 \cr & \Rightarrow 289 - {d^2} = 273 \cr & \Rightarrow {d^2} = 289 - 273 \cr & \Rightarrow {d^2} = 16 \cr & \Rightarrow {d^2} = {\left( { \pm 4} \right)^2} \cr & \therefore d = \pm 4 \cr & \because {\text{The A}}{\text{.P}}{\text{.}}\,{\text{is}}\,{\text{increasing}} \cr & \therefore d = 4 \cr & {\text{Now}}\,{\text{third}}\,{\text{term}} = a + d \cr & = 17 + 4 = 21 \cr}