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

MB
Answered by Meghan B. Maths tutor

4017 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find two values of k, such that the line y = kx + 2 is tangent to the curve y = x^2 + 4x + 3


When do I use the product rule as opposed to the chain rule?


Find the integral of 1/(x-5) with respect to x


How do you find the maximum/minimum value of an equation?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences