What is the sum of the first 500 odd numbers?
February 20th, 2023
##color(blue)(250000)##
The first odd number is ##color(blue)(1).##
The ##500^(th## odd number is:
(General formula of odd numbers is ##color(red)(t_n=2n-1##)
(Since n is 500)
##t_500=500*2-1=1000-1=color(blue)999##
The formula to calculate the sum of a given order is:
##color(red)(S_n=n/2(a+l)##
(Here,
S :-Sum
a :- first number
l :- last number)
So, we will do the math:
##S_500=500/2(1+999)=500/2*1000=250*1000=color(blue)(250000)##