After removing the first (10) odd natural numbers from the first (18) odd natural numbers, what is the sum of the remaining (8) numbers?
Answer and explanation
Correct answer: 224
The sum of the first n odd natural numbers is \(n^2\). Therefore, the sum of the first 18 odd numbers is \(18^2=324\), and the sum of the first 10 odd numbers is \(10^2=100\). Hence, the sum of the remaining 8 numbers is \(324-100=224\). A value such as 234 may result from an error in subtraction. Exam tip: when an initial set of terms is removed, subtract its sum from the total sum.
Frequently asked questions
What is the correct answer to this question?
224
Why is this the correct answer?
The sum of the first n odd natural numbers is \(n^2\). Therefore, the sum of the first 18 odd numbers is \(18^2=324\), and the sum of the first 10 odd numbers is \(10^2=100\). Hence, the sum of the remaining 8 numbers is \(324-100=224\). A value such as 234 may result from an error in subtraction. Exam tip: when an initial set of terms is removed, subtract its sum from the total sum.
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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