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SEQUENCES AND SERIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
MCQ
If three positive numbers are inserted between 4 and 512 such that the resulting sequence is a G.P., which of the following is not among the numbers inserted?
  • A
    256
  • B
    16
  • C
    64
  • ✓
    128
✓

Answer

Correct option: D.
128
  1. 128
Solution:
Let G.P. be $4, \mathrm{G}_1, \mathrm{G}_2, \mathrm{G}_3, 512$.
$\Rightarrow a=4 \text { and } a_5=a \times r^4=512 \times 4 \times r^4=512 \Rightarrow r^4$
$=\frac{512}{4}=128 \Rightarrow r=4 .$
$G_1=a_2=a \times r=4 \times 4=16 .$
$G_2=G_1 \times r=16 \times 4=64 .$
$G_3=G_2 \times r=64 \times 4=256 .$

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