Insert three numbers between 1 and 256 so that the resulting sequ… - Vidyadip

Question

Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.

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Answer

Suppose G₁, G₂, G₃ be three numbers between 1 and 256 such that 1, G₁,G₂, G₃, 256 is a G.P.
Thus, 256 = r⁴ giving r = $\pm$4 (Taking real roots only)
For r = 4, we have G₁ = ar = 4, G₂ = ar² = 16, G₃ = ar³ = 64
Similarly, for r = - 4, numbers are - 4,16 and - 64
Therefore,we can insert 4, 16, 64 between 1 and 256 so that the resulting sequences are in G.P.

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