After removing the first (14) odd natural numbers from the first (26) odd natural numbers, what will be the sum of the remaining numbers?
Answer and explanation
Correct answer: 480
The sum of the first n odd natural numbers is n². Therefore, the sum of the first 26 odd numbers is 26² and that of the first 14 odd numbers is 14². Remaining sum = 26² − 14² = 676 − 196 = 480. A value such as 468 may result from using an incorrect average for the 12 remaining terms. Exam tip: Recall directly that the sum of the first n consecutive odd numbers is n².
Frequently asked questions
What is the correct answer to this question?
480
Why is this the correct answer?
The sum of the first n odd natural numbers is n². Therefore, the sum of the first 26 odd numbers is 26² and that of the first 14 odd numbers is 14². Remaining sum = 26² − 14² = 676 − 196 = 480. A value such as 468 may result from using an incorrect average for the 12 remaining terms. Exam tip: Recall directly that the sum of the first n consecutive odd numbers is n².
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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