If (S_{n+3}-S_n=222), what is the value of (n)?
Answer and explanation
Correct answer: 72
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_{n+3}-S_n\) leaves only the next three terms: \((n+1)+(n+2)+(n+3)=3n+6\). Thus, \(3n+6=222\), so \(3n=216\) and \(n=72\). If \(n=74\), the difference would be \(228\), not 222. Exam tip: In the difference of two consecutive partial sums, cancel the common terms and add only the extra terms.
Frequently asked questions
What is the correct answer to this question?
72
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_{n+3}-S_n\) leaves only the next three terms: \((n+1)+(n+2)+(n+3)=3n+6\). Thus, \(3n+6=222\), so \(3n=216\) and \(n=72\). If \(n=74\), the difference would be \(228\), not 222. Exam tip: In the difference of two consecutive partial sums, cancel the common terms and add only the extra terms.
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.
