1000-1414-1732-2000-2236-?
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3000
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2441
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2892
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2449
The sequence follows the pattern √n × 1000. 1000 = √1 × 1000, 1414 ≈ √2 × 1000, 1732 ≈ √3 × 1000, 2000 = √4 × 1000, 2236 ≈ √5 × 1000. The next term is √6 × 1000 ≈ 2449.
To find the missing number in the given sequence, let's examine the differences between consecutive numbers:
1414 - 1000 = 414 1732 - 1414 = 318 2000 - 1732 = 268 2236 - 2000 = 236
Notice that the differences are decreasing by 96 each time.
To find the next difference, we subtract 96 from the previous difference: 236 - 96 = 140
Now, we can find the missing number by adding this difference to the last number in the sequence: 2236 + 140 = 2376
Therefore, the missing number in the sequence is 2376.
Looking at the options:
A. 3000 - This option is incorrect because it does not follow the pattern in the given sequence. B. 2441 - This option is incorrect because it does not follow the pattern in the given sequence. C. 2892 - This option is incorrect because it does not follow the pattern in the given sequence. D. 2449 - This option is correct because it follows the pattern in the given sequence.
The correct answer is D.