Chapter 9 Class 11 Sequences and Series
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 17 Deleted for CBSE Board 2024 Exams
Example 9 Important
Example 10 Important
Ex 8.2, 3 Important
Ex 8.2, 11 Important
Ex 8.2, 17 Important
Ex 8.2, 18 Important
Ex 8.2, 22 Important
Ex 8.2, 28 You are here
Ex 8.2, 29 Important
Ex 9.4.4 Important Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Deleted for CBSE Board 2024 Exams
Question 9 Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Misc 10 Important
Question 13 Important Deleted for CBSE Board 2024 Exams
Misc 14 Important
Misc 18 Important
Chapter 9 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Ex9.3, 28 The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3 + 2 2) :"(3 2 " 2) Introduction Componendo dividendo If / = / Applying componendo dividendo ( + )/( ) = ( + )/( ) Eg: Taking 1/2 = 4/8 (1+ 2)/(1 2) = (4 + 8)/(4 8) 3/( 1) = 12/( 4) -3 = -3 Ex 8.2, 28 The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3 + 2 2) :"(3 2 " 2) Let a & b be the numbers We know that Geometric mean of two numbers a & b is i.e. GM of a & b = According to the question Sum of two numbers a and b is 6 times of their GM a + b = 6 Solving, ( + )/(2 ) = 3/1 Applying componendo & dividendo ( + +2 )/( + 2 ) = (3 + 1)/(3 1 ) (( )2+( )2+2( ))/(( )2+( )2 2( ) ) = 4/2 Using (x + y)2 = x2 + y2 + 2xy (x - y)2 = x2 + y2 - 2xy ( + )2/( )2 = 2/1 (( + )/( ))^2 = 2/1 ( + )/( ) = 2/( 1) Again applying componendo & dividendo (( + )+( ))/(( + ) ( ) ) = ( 2 + 1)/( 2 1) ( + + )/( + + ) = ( 2 + 1)/( 2 1) (2 + 0)/( + + ) = ( 2 + 1)/( 2 1) (2 )/(2 + 0) = ( 2 + 1)/( 2 1) (2 )/(2 ) = ( 2 + 1)/( 2 1) ( / ) = ( 2 + 1)/( 2 1) Squaring both sides ( ( / ))^2 = (( 2 + 1)/( 2 1))^2 / = (( 2 + 1)2)/(( 2 1)2) / = (( 2)2 + (1)2 + 2 2 1)/(( 2)2 + (1)2 2 2 1) / = (2 + 1 + 2 2)/(2 + 1 2 2) / = (3 + 2 2)/(3 2 2) Thus the ratio of a & b is 3 + 2 3: 3 2 2 Hence proved