What is the average of all numbers between 11 and 80 which are divisible by 6?

Solution (By Examveda Team)

$$\eqalign{ & {\text{11 to 80 divisible by 6}} \cr & {\text{12, 18, }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. 78}} \cr & {\text{First term}}\left( a \right) = 12 \cr & {\text{Last term}}\left( l \right) = 78 \cr & {\text{Total number of terms}} \cr & = \frac{{{\text{Last term }} - {\text{ First term}}}}{{{\text{Common difference}}}} + 1 \cr & = \frac{{78 - 12}}{6} + 1 \cr & = 12 \cr & {\text{Average of 12 numbers}} \cr & = \frac{n}{2}\frac{{\left( {a + l} \right)}}{n} \cr & = \frac{{12 + 78}}{2} \cr & = 45 \cr} $$