If \(1+2+3+\cdots+n=1035\), what is the value of \(n\)?
Answer and explanation
Correct answer: 45
The left side is the sum of the first \(n\) natural numbers, so use \(n(n+1)/2=1035\). Testing the central options, \(n=45\) gives \(45\times46/2=45\times23=1035\). Therefore \(n=45\), and option C is correct. Algebraically, the equation becomes \(n^2+n-2070=0\), which factors as \((n-45)(n+46)=0\). Since \(n\) is a natural-number count, the valid solution is 45; the negative root is rejected. The neighboring options 43, 44, and 46 do not produce 1035 when substituted into the sum formula.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The left side is the sum of the first \(n\) natural numbers, so use \(n(n+1)/2=1035\). Testing the central options, \(n=45\) gives \(45\times46/2=45\times23=1035\). Therefore \(n=45\), and option C is correct. Algebraically, the equation becomes \(n^2+n-2070=0\), which factors as \((n-45)(n+46)=0\). Since \(n\) is a natural-number count, the valid solution is 45; the negative root is rejected. The neighboring options 43, 44, and 46 do not produce 1035 when substituted into the sum formula.
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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