The 3^rd and 7^th term of an arithmetic progression are -9 and 11 respectively. What is the 15^th term?

Solution (By Examveda Team)

$$\eqalign{ & {T_3} = a + 2d = - 9\,.....\,\left( 1 \right) \cr & {T_7} = a + 6d = 11\,.....\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 5\,\& \,a = - 19 \cr & {T_{15}} = a + 14d \cr & \,\,\,\,\,\,\,\,\,\, = - 19 + 14\left( 5 \right) \cr & \,\,\,\,\,\,\,\,\,\, = 51 \cr} $$