The average of 6 consecutive numbers (integers) is 19.5. What is the largest of these numbers?

Question: The average of 6 consecutive numbers (integers) is 19.5. What is the largest of these numbers?

Solution:
Let the 6 consecutive integers be:
x, x+1, x+2, x+3, x+4, x+5.

Their sum is:
Sum=x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=6x+15
To calculate the average, we use the average formula
Average: Summation/ total number
= 6x+15 / 6 = 19.5​

We multiply both sides by 6:
6x+15=117
⇒6x=102
⇒x=17

So the numbers are:
17, 18, 19, 20, 21, 22
- Largest number = 22.