What is the average of all numbers between 8 and 74 which are divisible by 7?

Solution (By Examveda Team)

$$\eqalign{ & 14,\,21\,......\,70 \cr & \mathop {8 - - - - - - - 74}\limits_{{\text{Divisible by 7}}} \cr & {\text{Number of items}} = \frac{{{\text{Lat term}} - {\text{First term}}}}{{{\text{Common Difference}}}} + 1 \cr & = \frac{{70 - 14}}{7} + 1 \cr & = 9 \cr & {\text{Average of all number divisible by 7}} \cr & \Rightarrow \frac{n}{{2 \times n}}\left[ {a + l} \right] \cr & \Rightarrow \frac{{84}}{2} \cr & \Rightarrow 2 \cr} $$