If (S_{2k+1}=1770), what will be the value of (k)?
Answer and explanation
Correct answer: 29
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(\frac{n(n+1)}{2}=1770\) gives \(n=59\), since \(\frac{59\times60}{2}=1770\). Therefore, \(2k+1=59\), so \(2k=58\) and \(k=29\). Option 30 may result from incorrectly taking the index as 60 instead of 59. Exam tip: first find n from \(S_n\), then equate the given index \(2k+1\) to n.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(\frac{n(n+1)}{2}=1770\) gives \(n=59\), since \(\frac{59\times60}{2}=1770\). Therefore, \(2k+1=59\), so \(2k=58\) and \(k=29\). Option 30 may result from incorrectly taking the index as 60 instead of 59. Exam tip: first find n from \(S_n\), then equate the given index \(2k+1\) to n.
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.
