If S_n=8911, where S_n is the sum of the first n natural numbers, what is the value of n?
Answer and explanation
Correct answer: 133
Apply S_n=n(n+1)/2 to the given sum. We need n(n+1)/2=8911, or n(n+1)=17822. The consecutive numbers 133 and 134 have product 133×134=17822. Therefore S_133=133×134/2=8911, so n=133 and option B is correct. Checking adjacent choices confirms the result: S_132=132×133/2=8778, while S_134=134×135/2=9045. Since the sequence of partial sums is strictly increasing, no second positive natural-number index can give 8911.
Frequently asked questions
What is the correct answer to this question?
133
Why is this the correct answer?
Apply S_n=n(n+1)/2 to the given sum. We need n(n+1)/2=8911, or n(n+1)=17822. The consecutive numbers 133 and 134 have product 133×134=17822. Therefore S_133=133×134/2=8911, so n=133 and option B is correct. Checking adjacent choices confirms the result: S_132=132×133/2=8778, while S_134=134×135/2=9045. Since the sequence of partial sums is strictly increasing, no second positive natural-number index can give 8911.
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.
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