The 2^nd and 8^th term of an arithmetic progression are 17 and -1 respectively. What is the 14^th term?

Solution (By Examveda Team)

$$\eqalign{ & {T_2} = a + d = 17\,.......\,\left( 1 \right) \cr & {T_8} = a + 7d = - 1\,......\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = - 3\,\& \,a = 20 \cr & {T_{14}} = a + 13d \cr & \,\,\,\,\,\,\,\,\,\, = 20 + 13\left( { - 3} \right) \cr & \,\,\,\,\,\,\,\,\,\, = - 19 \cr} $$