Example 21 - Chapter 9 Class 11 Sequences and Series (Term 1)
Last updated at May 29, 2018 by Teachoo
AP and GP mix questions
Chapter 9 Class 11 Sequences and Series (Term 1)
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
- Inserting GP between two numbers
- Geometric Mean (GM)
- AM and GM (Arithmetic Mean And Geometric mean)
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AP and GP mix questions
- Finding sum from series
- Finding sum from nth number
Transcript
Example 21 If pth, qth, rth and sth terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P. We know that the nth term of AP is a + (n – 1)d i.e. an = a + (n – 1)d It is given that ap, aq, ar & as in GP i.e. their common ratio is same So,𝑎_𝑞/𝑎_𝑝 = (ar )/qq = 𝑎𝑠/𝑎𝑟 We need to show (p – q), (q – r), (r – s) are in GP i.e. we need to show their common ratio is same i.e. we need to show (q − r )/(p − q) = (r − s )/(q − r) It is given (aq )/qp = (ar )/qq = (as )/ar From (A) & (B) (𝑞 − 𝑟)/(𝑝 − 𝑞) = (𝑟 − 𝑠)/(𝑞 − 𝑟) Hence (p – q), (q – r), (r – s) are in GP Hence proved
