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What is the average of all odd numbers between 1 and 100?
- a)51
- b)52
- c)50
- d)54
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the average of all odd numbers between 1 and 100?a)51b)52c)50d...
All odd numbers between 5 and 100 = 7 to 99
Hence, Option C is correct.
Hence, Option C is correct.
Most Upvoted Answer
What is the average of all odd numbers between 1 and 100?a)51b)52c)50d...
Understanding the Range of Odd Numbers
In the range from 1 to 100, the odd numbers are:
- 1, 3, 5, 7, 9, ..., 99.
These numbers form an arithmetic series where the first term (a) is 1, and the common difference (d) is 2.
Counting the Odd Numbers
To find how many odd numbers are there between 1 and 100:
- The last odd number is 99.
- The sequence of odd numbers can be expressed as:
- n = (last term - first term) / difference + 1
- n = (99 - 1) / 2 + 1 = 50.
So, there are a total of 50 odd numbers.
Calculating the Sum of Odd Numbers
Next, we calculate the sum of these odd numbers. The sum (S) of an arithmetic series is given by:
- S = n/2 * (first term + last term)
- S = 50/2 * (1 + 99)
- S = 25 * 100 = 2500.
Finding the Average
To find the average (A), we use the formula:
- A = Sum of all odd numbers / Total count of odd numbers
- A = 2500 / 50 = 50.
Thus, the average of all odd numbers between 1 and 100 is 50, which corresponds to option 'C'.
Conclusion
- The average of odd numbers from 1 to 100 is confirmed as 50.
- This understanding can help in similar arithmetic series problems in exams like SSC CHSL.
In the range from 1 to 100, the odd numbers are:
- 1, 3, 5, 7, 9, ..., 99.
These numbers form an arithmetic series where the first term (a) is 1, and the common difference (d) is 2.
Counting the Odd Numbers
To find how many odd numbers are there between 1 and 100:
- The last odd number is 99.
- The sequence of odd numbers can be expressed as:
- n = (last term - first term) / difference + 1
- n = (99 - 1) / 2 + 1 = 50.
So, there are a total of 50 odd numbers.
Calculating the Sum of Odd Numbers
Next, we calculate the sum of these odd numbers. The sum (S) of an arithmetic series is given by:
- S = n/2 * (first term + last term)
- S = 50/2 * (1 + 99)
- S = 25 * 100 = 2500.
Finding the Average
To find the average (A), we use the formula:
- A = Sum of all odd numbers / Total count of odd numbers
- A = 2500 / 50 = 50.
Thus, the average of all odd numbers between 1 and 100 is 50, which corresponds to option 'C'.
Conclusion
- The average of odd numbers from 1 to 100 is confirmed as 50.
- This understanding can help in similar arithmetic series problems in exams like SSC CHSL.
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What is the average of all odd numbers between 1 and 100?a)51b)52c)50d)54Correct answer is option 'C'. Can you explain this answer?
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