If S_n=n(n+1)/2 and S_n=6670, what is the value of n?
Answer and explanation
Correct answer: 115
Substitute the given value into the sum formula: n(n+1)/2=6670. Multiplying by 2 gives n(n+1)=13340. Among the choices, n=115 gives 115×116=13340, so 115×116/2=6670. Hence option C is correct. The neighboring values do not work: 110×111/2=6105, 112×113/2=6328, and 116×117/2=6786. Since n is a nonnegative counting index and n(n+1)/2 increases with n, no other listed value can satisfy the equation. Direct substitution is therefore sufficient and reliable.
Frequently asked questions
What is the correct answer to this question?
115
Why is this the correct answer?
Substitute the given value into the sum formula: n(n+1)/2=6670. Multiplying by 2 gives n(n+1)=13340. Among the choices, n=115 gives 115×116=13340, so 115×116/2=6670. Hence option C is correct. The neighboring values do not work: 110×111/2=6105, 112×113/2=6328, and 116×117/2=6786. Since n is a nonnegative counting index and n(n+1)/2 increases with n, no other listed value can satisfy the equation. Direct substitution is therefore sufficient and reliable.
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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