Question

Calculate the average of
all odd numbers
and average of all the
Even

numbers from 1 to 45
a )23,23 b) 21, 24 c)23,26
d) 23, 28​

Answer 1

Given,

The range of numbers = 1 to 45

To find,

The average of all even numbers of the given range and the average of all odd numbers of the given range.

Solution,

We can easily solve this mathematical problem by using the following mathematical process.

Now, we have to take the help of the AP series formula.

First term of AP in case of odd numbers = 1

Last term of AP in case of odd numbers = 45

Common difference = 2

Total number of terms = n

45 = 1+(n-1)×2

45 = 1+2n-2

45 = 2n-1

2n = 46

n = 23

Total number of odd numbers = 23

Total number of even numbers = (45-23) = 22

Sum of odd numbers = 23/2 [2×1+(23-1)×2]

= 23/2 (2+44)

= 23/2 × 46

= 529

Average of odd numbers = 529/23 = 23

Sum of even numbers = 22/2 [2×2+(22-1)×2]

= 22/2 (4+42)

= 11×46

= 506

Average of even numbers = 506/22 = 23

Hence, average of odd numbers is 23 and average of even numbers is 23.