If the 3^rd and the 5^th term of an arithmetic progression are 13 and 21, what is the 13^th term?

Solution (By Examveda Team)

$$\eqalign{ & {T_3} = a + 2d = 13\,.....\,\left( 1 \right) \cr & {T_5} = a + 4d = 21\,.....\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 4\& a = 5 \cr & {T_{13}} = a + 12d \cr & \,\,\,\,\,\,\,\,\, = 5 + 12\left( 4 \right) \cr & \,\,\,\,\,\,\,\,\, = 5 + 48 \cr & \,\,\,\,\,\,\,\,\, = 53 \cr} $$