If the sum of the first (n) natural numbers is (55), what will (n) be?
Answer and explanation
Correct answer: 10
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=55\), so \(n(n+1)=110\). Since \(10\times11=110\), \(n=10\). For instance, if \(n=9\), the sum is only \(\frac{9\times10}{2}=45\). Exam tip: use \(\frac{n(n+1)}{2}\) directly for sums of consecutive natural numbers.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=55\), so \(n(n+1)=110\). Since \(10\times11=110\), \(n=10\). For instance, if \(n=9\), the sum is only \(\frac{9\times10}{2}=45\). Exam tip: use \(\frac{n(n+1)}{2}\) directly for sums of consecutive natural numbers.
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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