What is the sum of the first 500 odd numbers?

##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)##