The 2^nd and 6^th term of an arithmetic progression are 8 and 20 respectively. What is the 20^th term?

Solution (By Examveda Team)

$$\eqalign{ & {T_2} = a + d = 8\,.......\,\left( 1 \right) \cr & {T_6} = a + 5d = 20\,......\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 3\,\& \,a = 5 \cr & {T_{20}} = a + 19d \cr & \,\,\,\,\,\,\,\,\,\, = 5 + 19\left( 3 \right) \cr & \,\,\,\,\,\,\,\,\,\, = 62 \cr} $$