The sum of the first (n) natural numbers is (13695). What is the value of (n-30)?
Answer and explanation
Correct answer: 135
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=13695\), so \(n(n+1)=27390\). Since \(165\times166=27390\), we get \(n=165\). Therefore, \(n-30=165-30=135\). Choosing 140 would mean \(n=170\), whose sum is not 13695. Exam tip: when a sum is given, first write \(2S=n(n+1)\) and look for two consecutive factors.
Frequently asked questions
What is the correct answer to this question?
135
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=13695\), so \(n(n+1)=27390\). Since \(165\times166=27390\), we get \(n=165\). Therefore, \(n-30=165-30=135\). Choosing 140 would mean \(n=170\), whose sum is not 13695. Exam tip: when a sum is given, first write \(2S=n(n+1)\) and look for two consecutive factors.
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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