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What is the average of all the natural numbers from 1 to 87?
45
44.5
43.5
44
44
For any sequence of consecutive natural numbers (arithmetic progression with common difference 1), the average is simply the midpoint of the first and last numbers.
Natural numbers from 1 to 87, where the first term a = 1 and the last term l = 87.
Average=2a+lтАЛ
For any sequence of consecutive natural numbers (arithmetic progression with common difference 1), the average is simply the midpoint of the first and last numbers.
Many students try to calculate the sum using SnтАЛ=2n(n+1)тАЛ and then divide by n, which is unnecessary work compared to the direct midpoint formula.
Identify parameters
Identify the first natural number as a=1 and the last natural number as l=87.
a=1,l=87
Apply average formula
Since the sequence is a consistent arithmetic progression, apply the formula for the mean of an AP: Average=(a+l)/2.
Average=21+87тАЛ
Calculate the result
Add the terms to get 88 and divide by 2 to reach the final average of 44.
Average=288тАЛ=44
D is correct because the average of consecutive numbers from 1 to 87 is calculated as (1 + 87) / 2 = 44.
This concept of the midpoint applies to any arithmetic progression (e.g., finding the average of all even numbers up to 100), which is a common shortcut in Data Interpretation and Average-based reasoning.
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