Example 17 - Insert three numbers between 1 and 256 - Examples

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  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Example 17 Insert three numbers between 1 and 256 so that the resulting sequence is a G.P. We know that to insert n numbers between a & b Than common ratio r = 𝑏﷮𝑎﷯﷯﷮ 1﷮𝑛+1﷯﷯ We need to insert 3 numbers between 1 & 256 Here a = 1 & b = 256 So r = 256﷮1﷯﷯﷮ 1﷮3+1﷯﷯ = (256)﷮ 1﷮4﷯﷯ = (4)﷮4 × 1﷮4﷯ ﷯ = ± 4 Thus, r = 4 and r = -4 Taking r = 4 Inserting numbers Hence the three numbers inserted are 4, 16 & 64 Hence the numbers inserted are 4, 16 & 64 for r = 4 & – 4, 16 & – 64 for r = – 4

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