The sum of seven consecutive odd numbers exceeds four times the largest by 15. Find the average of average of these numbers.

Question: The sum of seven consecutive odd numbers exceeds four times the largest by 15. Find the average of average of these numbers.

Solution:
Let the seven consecutive odd numbers be centered at n,
n - 6, n - 4, n - 2, n, n + 2, n + 4, n + 6

Sum of these consecutive odd numbers = n - 6 + n - 4 + n - 2 + n + n + 2 + n + 4 + n + 6 = 7n
And largest number = n + 6

ATQ,
7n = 4(n + 6) + 15
⇒ 7n = 4n + 24 + 15
⇒ 7n - 4n = 39
⇒ 3n = 39
∴ n = 13

∴ Average = 7n/7 = n = 13