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The average of 5 consecutive numbers is n. If the next two numbers are also included the average will
- a)increases by 1
- b)increases by 3
- c)increases by 1.5
- d)remain same
Correct answer is option 'A'. Can you explain this answer?
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The average of 5 consecutive numbers is n. If the next two numbers are...
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The average of 5 consecutive numbers is n. If the next two numbers are...
Explanation:
To solve this problem, let's assume that the first number in the sequence is x. Since the numbers are consecutive, the other four numbers will be x+1, x+2, x+3, and x+4.
Finding the average of the 5 numbers:
The average of a set of numbers is found by summing all the numbers and dividing by the total count. In this case, we have 5 numbers, so the average can be calculated as:
Average = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5
Simplifying the expression:
Average = (5x + 10) / 5
Average = x + 2
We are given that the average of these 5 numbers is n. So, we can write the equation:
x + 2 = n
Including the next two numbers:
If we include the next two numbers in the sequence, the average will be calculated based on all 7 numbers. Let's find the new average.
The next two numbers in the sequence will be (x+5) and (x+6). So, the new average can be calculated as:
New Average = (x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)) / 7
Simplifying the expression:
New Average = (7x + 21) / 7
New Average = x + 3
Comparing the averages:
We can see that the new average (x+3) is 1 unit greater than the original average (x+2). Therefore, the correct answer is option 'a' - the average increases by 1.
Conclusion:
When the next two numbers are included in the sequence, the average increases by 1. This can be observed by comparing the expressions for the original average (x+2) and the new average (x+3).
To solve this problem, let's assume that the first number in the sequence is x. Since the numbers are consecutive, the other four numbers will be x+1, x+2, x+3, and x+4.
Finding the average of the 5 numbers:
The average of a set of numbers is found by summing all the numbers and dividing by the total count. In this case, we have 5 numbers, so the average can be calculated as:
Average = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5
Simplifying the expression:
Average = (5x + 10) / 5
Average = x + 2
We are given that the average of these 5 numbers is n. So, we can write the equation:
x + 2 = n
Including the next two numbers:
If we include the next two numbers in the sequence, the average will be calculated based on all 7 numbers. Let's find the new average.
The next two numbers in the sequence will be (x+5) and (x+6). So, the new average can be calculated as:
New Average = (x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)) / 7
Simplifying the expression:
New Average = (7x + 21) / 7
New Average = x + 3
Comparing the averages:
We can see that the new average (x+3) is 1 unit greater than the original average (x+2). Therefore, the correct answer is option 'a' - the average increases by 1.
Conclusion:
When the next two numbers are included in the sequence, the average increases by 1. This can be observed by comparing the expressions for the original average (x+2) and the new average (x+3).
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The average of 5 consecutive numbers is n. If the next two numbers are also included the average willa)increases by 1b)increases by 3c)increases by 1.5d)remain sameCorrect answer is option 'A'. Can you explain this answer?
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