Question
What is the average of the squares of the first 23 natural
numbers?Solution
Sum of squares of first 'n' natural numbers = n × (n + 1) × (2n + 1) ÷ 6
So, average = n × (n + 1) × (2n + 1) ÷ 6n = (n + 1) × (2n + 1) ÷ 6
= (23 + 1) × (2 × 23 + 1) ÷ 6
= 24 × 47 ÷ 6
= 188
A Train Rajdhani Express leaves Kanpur station at 6 am and reaches Lucknow station at 10 am. Another Train Shatabdi Express leaves Lucknow station at 8 ...
- A man is running at a speed of 10 m/sec in the same direction of the train. Train can cross the man in 6 seconds. If speed of the train is 108 km/hr, then ...
A train with 10 compartments of equal length takes 20 seconds to cross a pole and 28 seconds to cross a 160-metre-long platform. If 4 compartments of th...
- A train moving at a speed of 50 m/s crosses a pole in 12 seconds. Determine the time required for the train to pass a 800-metre-long platform.
Two trains ‘A’ and ‘B’ started from station ‘P’ and ‘Q’ towards station ‘Q’ and ‘P’ respectively at the same time. When they met...
Two trains ‘A’ and ‘B’ started from station ‘P’ and ‘Q’ towards station ‘Q’ and ‘P’ respectively at the same time. When they met...
Train crosses a bridge which is 250 m long in 25 sec. Find the time taken by train to cross a man running in opposite direction at speed of 15m/sec. Fi...
Two trucks ‘M’ and ‘N’ started simultaneously from cities ‘X’ and ‘Y’ respectively towards each other. When they met after 9 hours, truc...
An early train leaves Chennai at a certain time. After 5 hours a Superfast Express leaves the same station and travels in the same direction at the spee...
- The distance between town A and town B is 555 km. A train leaves A at 7 a.m. at a speed of 60 km/h. Another train leaves B at 9 a.m. towards A at a speed o...
Relevant for Exams:
