If the sum of the first n natural numbers is 561, what is the value of n?
Answer and explanation
Correct answer: 33
The governing relationship is Sₙ = n(n + 1)/2 for the first n natural numbers. We seek the option whose product with its successor, divided by 2, equals 561. For n = 33, S₃₃ = 33 × 34/2 = 33 × 17 = 561. Therefore n = 33 and option C is correct. The neighboring choices confirm the uniqueness: S₃₂ = 32 × 33/2 = 528, whereas S₃₄ = 34 × 35/2 = 595. Since successive partial sums differ by the next natural number, the target 561 lies exactly at S₃₃. A common error is to use n²/2 or to forget the factor n + 1; the complete formula must be applied.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The governing relationship is Sₙ = n(n + 1)/2 for the first n natural numbers. We seek the option whose product with its successor, divided by 2, equals 561. For n = 33, S₃₃ = 33 × 34/2 = 33 × 17 = 561. Therefore n = 33 and option C is correct. The neighboring choices confirm the uniqueness: S₃₂ = 32 × 33/2 = 528, whereas S₃₄ = 34 × 35/2 = 595. Since successive partial sums differ by the next natural number, the target 561 lies exactly at S₃₃. A common error is to use n²/2 or to forget the factor n + 1; the complete formula must be applied.
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.
