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Ex 9.3, 6 - For what values of x, -2/7, x, -7/2 are in GP - Ex 9.3

Ex 9.3, 6 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 6 - Chapter 9 Class 11 Sequences and Series - Part 3

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Ex 9.3,6 For what values of x, the numbers (βˆ’2)/7, x, (βˆ’7)/2 are in G.P? Since (βˆ’2)/7, x, (βˆ’7)/2 are in GP So common ratio will be same Common ratio (r) = (π‘†π‘’π‘π‘œπ‘›π‘‘ π‘‘π‘’π‘Ÿπ‘š )/(πΉπ‘–π‘Ÿπ‘ π‘‘ π‘‘π‘’π‘Ÿπ‘š) = π‘₯/((βˆ’2)/7) = 7π‘₯/(βˆ’2) Also, Common ratio (r) = (π‘‡β„Žπ‘–π‘Ÿπ‘‘ π‘‘π‘’π‘Ÿπ‘š )/(π‘†π‘’π‘π‘œπ‘›π‘‘ π‘‘π‘’π‘Ÿπ‘š) = ((βˆ’7)/2)/π‘₯ = (βˆ’7)/2π‘₯ From (1) & (2) 7π‘₯/(βˆ’2) = (βˆ’7)/2π‘₯ 7x Γ— 2x = (-7) Γ— (-2) 14x2 = 14 x2 = 14/14 x2 = 1 x = Β± √1 x = Β±1 So, x = 1 or x = -1 GP is (βˆ’2)/7, x, (βˆ’7)/2 For x = 1, GP is (βˆ’2)/7, 1, (βˆ’7)/2 For x = –1, GP is (βˆ’2)/7, –1, (βˆ’7)/2 Hence possible numbers in GP are (βˆ’2)/7, 1, (βˆ’7)/2 or (βˆ’2)/7, –1, (βˆ’7)/2

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