Q 5 and 6

Q 5 and 6 o -27 (c) 13.5 (d) - 185 In of 21 terms the first II terms ure in AP with common dife:•— 2 and the last I I terms are in GP with common ratio 2, if the middle term AP is equal to the middle term GP, then the middle term of the entire 31 Thrw distinct numberg x, y, z form a GP in that order and the 7x • 5y, 7' 52, 72 form an AP in that order. The common ratio of GP (c) 10 (d) 18

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Please find below the solution to the asked query :

6 . Let the common ratio of GP be r . As x, y and z are in GP . So, y = xr, z = {xr}^{2} . . . (1) Now, 7 x + 5 y, 7 y + 5 z, 7 z + 5 x form an AP So, 2 (7 y + 5 z) = (7 x + 5 y) + (7 z + 5 x) 14 y + 10 z = 12 x + 5 y + 7 z 9 y + 3 z = 12 x 9 (xr) + 3 ({xr}^{2}) = 12 x (Using (i)) 3 r + r^{2} = 4 r^{2} + 3 r - 4 = 0 r^{2} + 4 r - r - 4 = 0 r (r + 4) - 1 (r + 4) = 0 (r - 1) (r + 4) = 0 S 0, r = 1 or r = - 4 Correct option is (a) - 4 .

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