For seven consecutive even numbers in a series, the difference between the square of the first and the last number of the series is 528. If the average of the third and fifth terms of the series is 'm' and the average of the second and sixth terms is 'n', then which of the following statement(s) is or are true?
I. m = n
II. (3m + 2n) is equal to 5 times of the fourth term of the series
III. (3m + 4) = (4n - 18)

Let the seven terms of the series be 'a', (a + 2) , (a + 4) , (a + 6) , (a + 8) , (a + 10) and (a + 12) respectively, ATQ; (a + 12) ² - a² = 528 a² + 24a + 144 - a² = 528 24a + 144 = 528 24a = 384 'a' = 16 So, the series = 16, 18, 20, 22, 24, 26, 28 'm' = {(20 + 24) /2} = (44/2) = 22 'n' = {(18 + 26) /2} = (44/2) = 22 Statement I: Since, the value of 'm' and 'n' are equal, which is 22. So, statement I is true. Statement II: (3m + 2n) = 3(22) + 2(22) = 66 + 44 = 110 Fourth term = 22 5 X 22 = 110 So, statement II is true. Statements III: (3m + 4) = 3(22) + 4 = 70 (4n - 18) = 4(22) - 18 = 70 So, statement III is true. Hence, option e.