Find n given S_n=124, a₁=19 and a_n=43

Solution (By Examveda Team)

Given, S_n=124, a₁=19 and a_n=43
Sum of an AP is given by:
$$ = {\text{Number}}\,{\text{of terms}} \times $$   $$\left\{ {\frac{{\left( {{\text{First}}\,{\text{term}} + {\text{Last}}\,{\text{term}}} \right)}}{2}} \right\}$$
$$\eqalign{ & 66 = {\text{n}} \times \left\{ {\frac{{\left( {{\text{a}} + {\text{l}}} \right)}}{2}} \right\} \cr & 124 = {\text{n}} \times \frac{{\left( {19 + 43} \right)}}{2} \cr & 124 = {\text{n}} \times \left( {\frac{{62}}{2}} \right) \cr & {\text{n}} = \frac{{\left( {124 \times 2} \right)}}{{62}} \cr & {\text{n}} = 4 \cr }$$