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Ex 8.2, 30 - Chapter 8 Class 11 Sequences and Series
Last updated at Dec. 16, 2024 by Teachoo
Geometric Progression(GP): Statement
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
Ex 8.2,30 The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour? Our sequence is 30, 60, 120, 240 . This is a G.P. as 60/30 = 2 & 120/60 = 2 Common ratio = 2 First term = 30 Thus, Bacteria present after 2 hours is a3 Bacteria present after 2 hours = a3 Now, an = arn-1 Putting a = 30, r = 2, n = 3 a3 = (30)(2)3 1 = (30) (2)2 = 30(4) = 120 Bacteria present after 4 hours = a5 Now, an = arn-1 Putting a = 30, r = 2, n = 5 a5 = (30)(2)5 1 = (30) (2)4 = 30 16 = 480 Bacteria present after nth hours = an+1 Now, an = arn 1 Putting a = 30, r = 2, n = n + 1 a5 = (30)(2)n + 1 1 = 30(2)n = (30) 2n Hence, Bacteria after 2nd hour = 120 Bacteria after 4th hour = 480 Bacteria after nth hour = 30(2n)
