Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
What is the average of all the natural numbers from 1 to 94?
48
47.5
47
48.5
47.5
For any sequence of numbers in Arithmetic Progression (AP), the average is simply the arithmetic mean of the first and last terms: 21+94тАЛ.
A sequence of natural numbers starting from 1 to 94.
Average=2First┬аTerm+Last┬аTermтАЛ
For any sequence of numbers in Arithmetic Progression (AP), the average is simply the arithmetic mean of the first and last terms: 21+94тАЛ.
Many students try to sum the numbers using the formula 2n(n+1)тАЛ and then divide by n, which is time-consuming and prone to calculation errors.
Identify the Sequence
The numbers are 1, 2, 3,..., 94, which form an Arithmetic Progression (AP) with the first term a=1 and the last term l=94.
a=1,l=94
Apply the Average Formula
Since the sequence is in AP, the average is the mean of the first and last terms.
Average=21+94тАЛ
Calculate the Final Result
Dividing the sum of the first and last terms by 2 gives the final average.
Average=295тАЛ=47.5
B is correct because the average of the first 94 natural numbers is calculated as 21+94тАЛ=47.5.
This formula works for any Arithmetic Progression (e.g., even numbers, odd numbers, or multiples of k); simply identify the first and last terms and divide their sum by 2.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants