If the sum of the first n natural numbers is Sₙ = 25,425, what is the value of n?
Answer and explanation
Correct answer: 225
The sum of the first n natural numbers is S_n=n(n+1)/2. Substituting the given sum gives n(n+1)/2=25425, so n(n+1)=50850. We need a consecutive pair of integers whose product is 50,850. Because n must be a natural number, checking the nearby option values is sufficient.
For n=225, n+1=226, and 225 times 226/2=225 times 113=25425. Thus the given sum is obtained exactly, so option C is correct. The neighboring values 224 and 226 would give different sums. The result is also sensible because the sum is approximately n^2/2, placing n near 225.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
The sum of the first n natural numbers is S_n=n(n+1)/2. Substituting the given sum gives n(n+1)/2=25425, so n(n+1)=50850. We need a consecutive pair of integers whose product is 50,850. Because n must be a natural number, checking the nearby option values is sufficient.
For n=225, n+1=226, and 225 times 226/2=225 times 113=25425. Thus the given sum is obtained exactly, so option C is correct. The neighboring values 224 and 226 would give different sums. The result is also sensible because the sum is approximately n^2/2, placing n near 225.
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.
