Question

The average of a set of 18 consecutive integers is 22.5. What is the smallest integer in the set?

Answer 1

total of these integers=22.5*18=405
let first integer =a
then last integer=a+17
then sum of 18 integers
\[=\frac{ 18*\left( a+a+17 \right) }{ 2 }=18a+153\]
\[[S _{n}=\frac{ n \left( a+l \right) }{ 2 }]\]
18a+153=405
find a