Question
What will be the geometric mean of 'Q' and 'P -
Q'. Two number series 'l' and 'II' are given below. Both series have a missing term, if 'P' and 'Q' are natural numbers, then find their values and answer the questions based on it. l. 13, 95, 218, 'P' , 619, 913 II. 108, 122, 143, 178, (Q2 + 2)  , 304Solution
ATQ, For I: 13 + (92 + 1) = 95 95 + (112 + 2) = 218 218 + (132 + 3) = 390 390 + (152 + 4) = 619 619 + (172 + 5) = 913 So, 'A' = 390 For II: 108 + (2 X 7) = 122 122 + (3 X 7) = 143 143 + (5 X 7) = 178 178 + (7 X 7) = 227 277 + (7 X 11) = 304 So, Q2 + 2 = 227 Or, Q2 = 225 So, 'Q' = ±15 Since, 'Q' is a natural number, therefore 'Q' = 15. 'Q' = 15 So, 'P- Q' = 390 - 15 = 375 So, required value = "(15 X 375) = 75
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