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Subjects
Class 9MathematicsSequences and ProgressionsSum of first n natural numbersHardLevel 60

When is the sum \(S_n\) of the first n natural numbers odd?

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Answer and explanation

Correct answer: When n leaves remainder 1 or 2 on division by 4

Using \(S_n=\frac{n(n+1)}{2}\), the sum is odd when n leaves remainder 1 or 2 on division by 4. Remainders 0 and 3 give an even sum. Exam tip: memorise this mod-4 pattern.

Tags

natural numberssum of n termstriangular numbersparitymodular arithmeticsequences and progressions

Frequently asked questions

What is the correct answer to this question?

When n leaves remainder 1 or 2 on division by 4

Why is this the correct answer?

Using \(S_n=\frac{n(n+1)}{2}\), the sum is odd when n leaves remainder 1 or 2 on division by 4. Remainders 0 and 3 give an even sum. Exam tip: memorise this mod-4 pattern.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.

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