Question
Consider a sequence (8, 11, 14, 17, 20, … up to 2020
terms). If P represents the average of all positive even integers and Q represents the average of all positive odd integers, find the difference between P and Q, where n is an integer greater than 198.Solution
If, we take 4 terms = 8, 11, 14, 17 Value of P = (8 + 14)/2 = 11 Value of Q = (11 + 17)/2 = 14 Difference of P and Q = 14 – 11 = 3 If we take 6 terms = 8, 11, 14, 17, 20, 23 Value of P = (8 + 14 + 20)/3 = 14 Value of Q = (11 + 17 + 23)/3 = 17 Difference of P and Q = 17 – 14 = 3 If we take 2020 terms, the difference will be the same = 3 Hence answer is option B
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