Misc 3 - Chapter 8 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Geometric Progression(GP): Formulae based
Ex 8.2, 6
Example 4
Ex 8.2, 1
Example 5 Important
Ex 8.2, 5 (a)
Ex 8.2, 2
Example 6
Ex 8.2, 4
Ex 8.2, 3 Important
Ex 8.2, 17 Important
Example 7 Important
Ex 8.2, 7 Important
Ex 8.2, 10
Ex 8.2, 9 Important
Ex 8.2, 11 Important
Ex 8.2, 8
Ex 8.2, 19
Ex 8.2, 20
Example 8
Ex 8.2, 13
Ex 8.2, 15
Ex 8.2, 16 Important
Ex 8.2, 21
Ex 8.2, 14 Important
Misc 3 You are here
Misc 2
Example 9 Important
Ex 8.2, 12
Example 10 Important
Ex 8.2, 18 Important
Misc 11 (i) Important
Misc 5
Misc 1 Important
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
- 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
Misc 3 The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P. It is given that Sum of third term & fifth term is 90 i.e. a3 + a5 = 90 We know that nth term of GP = arn – 1 i.e. an = arn – 1 Putting n = 3 & a = 1 a3 = 1 r3 – 1 = r2 Putting n = 5 & a = 1 a5 = 1.r5 – 1 a5 = r4 Putting a3 & a5 in (1) a3 + a5 = 90 r2 + r4 = 90 r4 + r2 – 90 = 0 Let r2 = x So, our equation becomes x2 + x – 90 = 0 x2 + 10x – 9x – 90 = 0 x(x + 10) – 9(x + 10) = 0 (x – 9)(x + 10) = 0 (x – 9)(x + 10) = 0 Hence the common ratio is -3 and 3
