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Ex 8.2, 26 - Chapter 8 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Inserting GP between two numbers
Chapter 8 Class 11 Sequences and Series
Concept wise
- Finding Sequences
- Arithmetic Progression (AP): Formulae based
- Arithmetic Progression (AP): Statement
- Arithmetic Progression (AP): Calculation based/Proofs
- Inserting AP between two numbers
- Arithmetic Mean (AM)
- Geometric Progression(GP): Formulae based
- Geometric Progression(GP): Statement
- Geometric Progression(GP): Calculation based/Proofs
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Inserting GP between two numbers
- Geometric Mean (GM)
- AM and GM (Arithmetic Mean And Geometric mean)
- AP and GP mix questions
- Finding sum from series
- Finding sum from nth number
Transcript
Ex 8.2, 26 Insert two numbers between 3 and 81 so that the resulting sequence is G.P. We know that to insert n numbers between a & b Common ratio r = ( / )^(1/( +1)) We need to insert 2 numbers between 3 & 81 Here a = 3 & b = 81 & n = number of terms to be inserted = 2 So r = (81/3)^(1/(2+1)) = (27) ^(1/3) = (3) ^(3 1/3 ) = 3 Ex 8.2, 26 Insert two numbers between 3 and 81 so that the resulting sequence is G.P. We know that to insert n numbers between a & b Common ratio r = ( / )^(1/( +1)) We need to insert 2 numbers between 3 & 81 Here a = 3 & b = 81 & n = number of terms to be inserted = 2 So r = (81/3)^(1/(2+1)) = (27) ^(1/3) = (3) ^(3 1/3 ) = 3 Thus, a = 3 , r = 3, b = 81 Inserting numbers Hence the two numbers inserted between 1 & 81 are 9 & 27 Thus, a = 3 , r = 3, b = 81 Inserting numbers Hence the two numbers inserted between 1 & 81 are 9 & 27
