If S_(2k+3) = 3240, what is the value of k?
Answer and explanation
Correct answer: 38.5
Let m = 2k + 3. Since S_m = m(m+1)/2 and S_m = 3240, we need m(m+1) = 6480. The consecutive integers 80 and 81 have product 80 × 81 = 6480, so m = 80. Therefore 2k + 3 = 80, which gives 2k = 77 and k = 77/2 = 38.5. Thus option D is correct. The earlier integer-only choices would make the item inconsistent, because the equation does not yield an integer k. The revised options include the exact value and preserve one unambiguous answer.
Frequently asked questions
What is the correct answer to this question?
38.5
Why is this the correct answer?
Let m = 2k + 3. Since S_m = m(m+1)/2 and S_m = 3240, we need m(m+1) = 6480. The consecutive integers 80 and 81 have product 80 × 81 = 6480, so m = 80. Therefore 2k + 3 = 80, which gives 2k = 77 and k = 77/2 = 38.5. Thus option D is correct. The earlier integer-only choices would make the item inconsistent, because the equation does not yield an integer k. The revised options include the exact value and preserve one unambiguous answer.
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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