If X is the n^th term of the given series and 'Y' is the (n + 1)^th term of the given series, choose the correct statement from the following options (i), (ii), and (iii). Given series: 763, 379, 187, 91, 43, 19, 7 (i) X = 2Y + 5 (ii) Y = 3X - 6 (iii) The difference between the 1^st and 2^nd term is twice the difference between the 2^nd and 3^rd term and so on.

Let's analyze the given statements against the series. For statement (i), if X is the nth term and Y is the (n+1)th term, we test X = 2Y + 5 with the first terms: 763 = 2(379) + 5, which holds true. We check the next terms: 379 = 2(187) + 5, which also holds true for the entire series. For statement (iii), the difference between the first and second term is 384, and the difference between the second and third is 192, showing the first difference is exactly twice the second. This halving pattern continues throughout the series. Statement (ii) is incorrect because 379 does not equal 3(763) - 6. Therefore, only statements (i) and (iii) are correct.

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