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What is the difference between the average of the first 79 natural numbers and the average of the first 39 natural numbers?
- a)19
- b)20
- c)39
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the difference between the average of the first 79 natural num...
∵ Sum of the first n natural numbers = n(n + 1)/2
⇒ Average of the first n natural numbers = n(n + 1)/2 × 1/n = (n + 1)/2
⇒ Average of the first n natural numbers = n(n + 1)/2 × 1/n = (n + 1)/2
Hence,
Average of the first 79 natural numbers = (79 + 1)/2 = 80/2 = 40
Average of the first 39 natural numbers = (39 + 1)/2 = 40/2 = 20
∴ Required difference = 40 - 20 = 20
Average of the first 79 natural numbers = (79 + 1)/2 = 80/2 = 40
Average of the first 39 natural numbers = (39 + 1)/2 = 40/2 = 20
∴ Required difference = 40 - 20 = 20
Most Upvoted Answer
What is the difference between the average of the first 79 natural num...
The average of a set of numbers is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set. In this case, we need to find the average of the first 79 natural numbers and the average of the first 39 natural numbers.
To find the average of the first 79 natural numbers, we can use the formula for the sum of an arithmetic series. The sum of the first n natural numbers is given by the formula:
Sum = (n/2)(first term + last term)
For the first 79 natural numbers, the first term is 1 and the last term is 79. Plugging these values into the formula, we get:
Sum = (79/2)(1 + 79) = (79/2)(80) = 3160
To find the average, we divide the sum by the number of terms, which in this case is 79:
Average = Sum/Number of terms = 3160/79 = 40
So, the average of the first 79 natural numbers is 40.
Next, we need to find the average of the first 39 natural numbers. Using the same formula, we can find the sum:
Sum = (39/2)(1 + 39) = (39/2)(40) = 780
To find the average, we divide the sum by the number of terms, which in this case is 39:
Average = Sum/Number of terms = 780/39 = 20
So, the average of the first 39 natural numbers is 20.
Therefore, the difference between the average of the first 79 natural numbers and the average of the first 39 natural numbers is:
40 - 20 = 20
Hence, the correct answer is option B) 20.
To find the average of the first 79 natural numbers, we can use the formula for the sum of an arithmetic series. The sum of the first n natural numbers is given by the formula:
Sum = (n/2)(first term + last term)
For the first 79 natural numbers, the first term is 1 and the last term is 79. Plugging these values into the formula, we get:
Sum = (79/2)(1 + 79) = (79/2)(80) = 3160
To find the average, we divide the sum by the number of terms, which in this case is 79:
Average = Sum/Number of terms = 3160/79 = 40
So, the average of the first 79 natural numbers is 40.
Next, we need to find the average of the first 39 natural numbers. Using the same formula, we can find the sum:
Sum = (39/2)(1 + 39) = (39/2)(40) = 780
To find the average, we divide the sum by the number of terms, which in this case is 39:
Average = Sum/Number of terms = 780/39 = 20
So, the average of the first 39 natural numbers is 20.
Therefore, the difference between the average of the first 79 natural numbers and the average of the first 39 natural numbers is:
40 - 20 = 20
Hence, the correct answer is option B) 20.
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What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer?
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What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer?.
What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between the average of the first 79 natural numbers and the average of thefirst 39 natural numbers?a)19b)20c)39d)40Correct answer is option 'B'. Can you explain this answer?.
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