The sum of the first K natural numbers is 300. Find the value of K.
S= 0.5n(n+1) ( formula for the sum of the first n natural numbers) 0.5K(K+1)= 300 ( sub in K and make the formula equal to the total sum given) 0.5K(K+1)-300= 0 ( take away 300 from both sides) 0.5K2 + 0.5K -300= 0 (expand brackets) K2 + K - 600=0 (multiply equation by a factor 2 to get rid of 0.5) (K + 25)(K - 24) = 0 (factorize equation) K = 24 or -25 Given that K must be positive, K= 24
