Question:
If the average of three consecutive odd numbers is 25, then find the numbers.
Correct Answer
23, 25, and 27
Solution And Explanation
Solution
Shortcut Trick to find the numbers if the average of three consecutive numbers are given
Here, given
The average of three consecutive odd numbers = 25
This means the number lies in the middle of the given three consecutive numbers will be the average
Therefore, number lies in middle of the given three consecutive odd numbers = 25
We can get the next consecutive odd number by addition of 2 to the number lies in the middle, and previous consecutive odd number by subtracting 2 to the number lies in the middle.
Therefore, the first odd number among the given three consecutive odd numbers
= Number in the middle – 2
= 25 – 2 = 23
And, last odd number among the given three consecutive numbers
= Number in the middle + 2
= 25 + 2 = 27
Thus, numbers are 23, 25, and 27 Answer
Procedure to find the numbers if the average of three consecutive odd numbers are given
It is necessary to know the procedure, as it applies to solving all similar types of given problems, as shortcut tricks are not applicable everywhere.
Given, the average of three consecutive odd numbers = 25
Thus, the smallest and the greatest number among the given three odd numbers = ?
Let first odd number = a
Therefore, the second consecutive odd number = a + 2
And, the third consecutive odd number = a + 4
Now,
Formula to find the
Average = Sum of observations/Numbers of observations
Therefore, the average of the given three consecutive odd numbers
= Sum of the three consecutive odd numbers/3
⇒ 25 = a+(a+2)+(a+4)/3
⇒ 25 = a+a+2+a+4/3
⇒ 25 = 3a + 6/3
After taking 3 as common from the numerator
⇒ 25 = 3 (a + 2)/ 3
⇒ 25 = a + 2
⇒ a + 2 = 25
After transposing 2 to RHS
⇒ a = 25 – 2
⇒ a = 23
Thus, first odd number = 23
And, the second consecutive odd number = a + 2
= 23 + 2 = 25
And, the 3rd and odd number = a + 4
= 23 + 4 = 27
Therefore, the given consecutive three odd numbers = 23, 25 and 27 Answer
Similar Questions
(1) Find the average of odd numbers from 9 to 949
(2) Find the average of the first 3005 odd numbers.
(3) Find the average of the first 3636 odd numbers.
(4) Find the average of odd numbers from 9 to 1375
(5) Find the average of even numbers from 6 to 1744
(6) Find the average of odd numbers from 3 to 1001
(7) Find the average of the first 3463 even numbers.
(8) Find the average of odd numbers from 13 to 1451
(9) Find the average of even numbers from 8 to 1210
(10) Find the average of odd numbers from 11 to 31