mathcity.org Merging man and maths Exercise 6.3 (Solutions) Textbook of lgebra and Trigonometry for Class XI Available online @ http://www.mat hcity.org, Version: 1.0.0 Question # 1 (i) 35 and 55 Here 3 5 a= and 55 b= , so A.M. 35 55 8 5 4 5 2 2 2 a b + + = = = = (ii) Same as (i) and (ii) (iii)2 1 x x − + and 2 1 x x + + Here 2 1 a x x = − + and 2 1 b x x = + + A.M. 2 2 2 2 1 1 2 2 1 2 2 2 a b x x x x x x + − + + + + + = = = = + Question # 2Since 5, 8 are two A.Ms between aand b. Therefore a, 5, 8, bare in A.P. Here 1 a a = and d= 8 – 5 = 3 Now 2 1 a a d= + 5 3 5 3 2 a a a ⇒ = + ⇒ − = ⇒ = Also 4 1 3 a a d= + 2 3(3) 11 b b ⇒ = + ⇒ = Question # 3Let 1 2 3 4 5 , , , , A A A A A and 6 are six A.Ms between 2 and 5. Then 1 2 3 4 5 6 2, , , , , , ,5 A A A A A are in A.P. Here 1 2 a = and 8 5 a = 1 7 5 a d⇒ + = 2 7 5 d⇒ + = 3 7 5 2 7 3 7 d d d⇒ = − ⇒ = ⇒ = So 1 2 1 3 17 2 7 7 A a a d= = + = + = ( ) 2 3 1 3 6 20 2 2 2 2 7 7 7 A a a d= = + = + = + = ( ) 3 4 1 3 9 23 3 2 3 2 7 7 7 A a a d= = + = + = + = ( ) 4 5 1 3 26 12 4 2 4 2 7 7 7 A a a d= = + = + = + = ( ) 5 6 1 3 15 29 5 2 5 2 7 7 7 A a a d= = + = + = + = ( ) 6 7 1 3 18 32 6 2 6 2 7 7 7 A a a d= = + = + = + = Hence 17 20 23 26 29 32 , , , , , 7 7 7 7 7 7 are six A.Ms between 2 and 5. Question # 4 Suppose 1 2 3 , , A A and 4 are four A.Ms between 2 and 12 2 . Then 1 2 3 4 12 2 , , , , , 2 A A A A are in A.P. Here 1 2 a = and 6 12 2 a =
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