1.

(a) Find x if the following numbers are in A.P(1) 4, x, 12(2) 2, (x − 1), 4(3) 6 − a, x, 6 + a(b) Find x if the following numbers are in G.P(1) 16, x, 25(2) 5, x + 1, 20(c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers(a) 1 and 4(b) 2 and 8(c) 9 and 16Verify that (i) A, G, H are in G.P, (ii) A > G > H.

Answer»

(a) Find x if the following numbers are in A.P



(1) 4, x, 12



(2) 2, (x − 1), 4



(3) 6 − a, x, 6 + a



(b) Find x if the following numbers are in G.P



(1) 16, x, 25



(2) 5, x + 1, 20



(c) If A, G, H are A.M, G.M, and H.M of the following pair of numbers



(a) 1 and 4



(b) 2 and 8



(c) 9 and 16



Verify that (i) A, G, H are in G.P, (ii) A > G > H.



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