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What is the average of all the natural numbers from 1 to 95?
49
48
48.5
47.5
48
For any series of consecutive natural numbers, the average is simply the mean of the first and the last term: (1 + 95) / 2 = 96 / 2 = 48.
Natural numbers from 1 to 95.
Average=2n+1тАЛ
For any series of consecutive natural numbers, the average is simply the mean of the first and the last term: (1 + 95) / 2 = 96 / 2 = 48.
Many students calculate the sum first using n(n+1)/2 and then divide by n, which is unnecessarily time-consuming and prone to calculation errors compared to the simple average formula.
Identify the Series
The numbers 1, 2, 3,..., 95 form an Arithmetic Progression (AP) where the first term a=1 and the last term l=95.
a=1,l=95
Apply Average Formula for AP
For any arithmetic sequence, the average is the mean of the first and the last term.
Average=2a+lтАЛ
Calculate the Result
Substitute the values a=1 and l=95 into the formula: Average=(1+95)/2=96/2.
Average=48
B is correct because the average of consecutive numbers from 1 to 95 is calculated as (1 + 95) / 2, which equals 48.
This property of Arithmetic Progressions is highly useful in time-saving for questions involving sums of series in Quantitative Aptitude exams.
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