The sum of the first (n) natural numbers is (10878). What is the value of (n-25)?
Answer and explanation
Correct answer: 122
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Hence, \(\frac{n(n+1)}{2}=10878\), so \(n(n+1)=21756\). Since \(147\times148=21756\), \(n=147\). Therefore, \(n-25=147-25=122\). Thus, option C is correct. A nearby choice such as 120 would give \(n=145\), whose sum is not 10878. Exam tip: after using \(n(n+1)/2\), look for two consecutive integers whose product equals twice the given sum.
Frequently asked questions
What is the correct answer to this question?
122
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Hence, \(\frac{n(n+1)}{2}=10878\), so \(n(n+1)=21756\). Since \(147\times148=21756\), \(n=147\). Therefore, \(n-25=147-25=122\). Thus, option C is correct. A nearby choice such as 120 would give \(n=145\), whose sum is not 10878. Exam tip: after using \(n(n+1)/2\), look for two consecutive integers whose product equals twice the given sum.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
