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Sequences and Series — MATHS STD 11 Science — Question

Rajasthan 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
  • D
    128
✓

Answer

  1. 128

Solution:

Let G.P. be 4, G1,  G2,  G3,  512.

⇒ a = 4 and a5 = a × r4 = 512 × 4 × r4 = 512 ⇒  r4

$=\frac{512}{4}=128\Rightarrow\text{r=4.}$

G1 = a2 = a × r = 4 × 4 = 16.

G2 = G1 × r = 16  × 4 = 64.

G3 = G2 × r = 64 × 4 = 256.

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