Given: The difference between the sum of four consecutive odd numbers and the sum of three consecutive even numbers is 12 The smallest even number is x Formula used: Average = Sum of observations/Number of observations Calculation: Let the smallest odd number be x + 1 ⇒ Four consecutive odd number = x + 1, x + 3, x + 5, x + 7 ⇒ Three consecutive even number = x, x + 2, x + 4 The sum of three consecutive even numbers is = x + (x + 2) + (x + 4) ⇒ 3x + 6 The sum of four consecutive odd numbers is = (x + 1) + (x + 3) + (x + 5) + (x + 7) ⇒ 4x + 16 According to question, we have ⇒ (4x + 16) – (3x + 6) = 12 ⇒ (4x – 3x) – (16 – 6) = 12 ⇒ x + 10 = 12 ⇒ x = 12 – 10 ⇒ x = 2 ⇒ Five consecutive odd numbers = 3, 5, 7, 9 ⇒ Next Five consecutive odd numbers = 11, 13, 15, 17, 19 We know that, Average = Sum of observations/Number of observations ⇒ Average = (11 + 13 + 15 + 17 + 19)/5 ⇒ Average = 75/5 ⇒ Average = 15 ∴ The average of the next five consecutive odd numbers is 15. [ alt="shortcut" src="//storage.googleapis.com/tb-img/production/21/04/shortcut.png" style="width: 225px; height: 48px;"> The average of odd number of consecutive number is the middle number of the series. 11, 13, 15, 17, 19 ∴ The average is 15 because it is in the middle position.