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Total rent paid for 10 days = Sum of the sequence 50 + 100 + 150 + …….. + 500

To find the sum of the sequence, we factor out 50 and write it as 50 ( 1 + 2 + 3 + …. 10).

The expression inside the bracket represents the sum of the first 10 positive integers.
Sum of first n positive integers = \(\frac{n (n + 1) }{ 2}\).

Therefore, value of (1 + 2 + 3 + … +10) = \(\frac{10 * 11 }{ 2}\) and hence,

Sum of the sequence = 50 * \(\frac{(10 * 11) }{ 2}\) = 50 * 5 * 11.

The answer has to be a multiple of 11 and there’s only one such value : 2750.

The correct answer option is A.

Hope that helps!
Aravind B T
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