If S_n+S_(n−1)=4212 and S_n−S_(n−1)=65, what is the value of S_n?
Answer and explanation
Correct answer: 2138.5
Treat S_n and S_(n−1) as two unknown quantities. Adding the two given equations eliminates S_(n−1): (S_n+S_(n−1))+(S_n−S_(n−1))=4212+65, so 2S_n=4277. Dividing by 2 gives S_n=2138.5, which is option A. Subtracting the equations would give 2S_(n−1)=4147, confirming the algebra. There is a noteworthy consistency issue: if S_n denotes the sum of the first n natural numbers, it should be an integer, so the supplied data cannot correspond to an actual natural-number index n. Nevertheless, the simultaneous equations uniquely determine the listed value.
Frequently asked questions
What is the correct answer to this question?
2138.5
Why is this the correct answer?
Treat S_n and S_(n−1) as two unknown quantities. Adding the two given equations eliminates S_(n−1): (S_n+S_(n−1))+(S_n−S_(n−1))=4212+65, so 2S_n=4277. Dividing by 2 gives S_n=2138.5, which is option A. Subtracting the equations would give 2S_(n−1)=4147, confirming the algebra. There is a noteworthy consistency issue: if S_n denotes the sum of the first n natural numbers, it should be an integer, so the supplied data cannot correspond to an actual natural-number index n. Nevertheless, the simultaneous equations uniquely determine the listed value.
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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