The first term of an Arithmetic Progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are:

Solution (By Examveda Team)

Number of terms = n (let)
First term (a) = 22
Last term (l) = - 11
Sum = 66
Sum of an AP is given by:
$$ = {\text{Number}}\,{\text{of terms}}\,\, \times $$    $$ {\frac{{ {{\text{First}}\,{\text{term}} + {\text{Last}}\,{\text{term}}} }}{2}} $$
$$\eqalign{ & 66 = {\text{n}} \times {\frac{{ {{\text{a}} + {\text{l}}} }}{2}} \cr & 66 = {\text{n}} \times \frac{{ {22 - 11} }}{2} \cr & 66 = {\text{n}} \times {\frac{{11}}{2}} \cr & {\text{n}} = \frac{{ {66 \times 2} }}{{11}} \cr & {\text{n}} = 12 \cr & {\text{No}}{\text{.}}\,{\kern 1pt} {\text{of}}\,{\text{terms}} = 12 \cr} $$