Sequences and Series — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
Question
Insert three numbers between $1$ and $256$ so that the resulting sequence is a G.P.
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Answer
Suppose $G_1, G_2, G_3 $ be three numbers between 1 and 256 such that $1, G_1,G_2, G_3, 256$ is a G.P.
Thus, $256 = r^4 $ giving $r = \pm4 ($Taking real roots only$)$
For $r = 4$, we have $G_1 = ar = 4, G_2 = ar^2 = 16, G_3 = ar^3 = 64$
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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