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Ex 9.3, 5 - Which term of following sequences - Chapter 9 - Geometric Progression(GP): Formulae based

Ex 9.3, 5 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 5 - Chapter 9 Class 11 Sequences and Series - Part 3

 

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Transcript

Ex9.3, 5 Which term of the following sequences: 2, 2 2, 4, is 128 2, 2 2, 4, We know that an = arn 1 where an = nth term of GP n is the number of terms a is the first term r is the common ratio Here, First term a = 2 , Common ratio r = (2 2)/2 = 2 nth term = 128 Putting values nth term = arn-1 128 = (2)( 2)^( 1) 128/2 = ( 2)^( 1) 64 = ( 2)^( 1) 26 = ( 2)^( 1) Squaring both sides (26)2 =[( 2)^( 1) ]^2 26 2 = [( 2)^2 ]^( 1) 212 = [2]^( 1) Comparing powers 12 = n 1 12 + 1 = n 13 = n n = 13 Hence, 13th term of GP is 128

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