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
The average of the first 30 natural numbers is:
15
16
15.5
16.5
15.5
For any sequence of consecutive natural numbers starting from 1 up to n, the average is simply the midpoint of the first and last term: (First + Last) / 2.
The sequence consists of the first 30 natural numbers, meaning the set is {1, 2, 3,..., 30}. The total number of terms n = 30.
Average=2n+1тАЛ
For any sequence of consecutive natural numbers starting from 1 up to n, the average is simply the midpoint of the first and last term: (First + Last) / 2.
Students often mistakenly calculate the sum up to 30 as 30*30/2 = 450 and then divide by 29 instead of 30, or get confused by the 'first n natural numbers' definition.
Identify the parameters
Identify that the set is an arithmetic progression where the first term a=1 and the last term l=30. The number of terms is n=30.
n=30
Apply the average formula
Since natural numbers form an arithmetic progression, the average is the mean of the first and last term.
Average=21+30тАЛ
Calculate the result
Divide the sum of the first and last terms by 2.
Average=231тАЛ=15.5
C is correct because the average of the first 30 natural numbers is calculated as 31 divided by 2, resulting in 15.5.
This concept is a subset of the Average topic; remember that for any arithmetic progression, the average is always (First Term + Last Term) / 2, which helps in solving complex series questions quickly.
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