The average of 15 consecutive natural numbers arranged in ascending order is…
2025
The average of 15 consecutive natural numbers arranged in ascending order is A. The average of the first 11 of these numbers is:
- A.
A-1
- B.
A-2
- C.
A-3
- D.
A-4
- E.
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Correct answer: B
To find the average of the first 11 numbers, we first need to understand the structure of the 15 consecutive natural numbers.
Step-by-Step Analysis
Define the sequence: Let the 15 consecutive natural numbers be:
x, x+1, x+2, ..., x+14.
Use the average property: For any arithmetic progression, the average is the middle term.
With 15 terms, the middle term is the 8th term.
The 8th term is x + 7.
Therefore, the average (A) = x + 7, which means x = A - 7.
Analyze the first 11 numbers: These are:
x, x+1, x+2, ..., x+10.
The average of these 11 numbers is the middle term, which is the 6th term.
The 6th term is x + 5.
Substitute x:
Substitute x = A - 7 into the expression for the new average:
New average = (A - 7) + 5 = A - 2.