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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
If $\alpha ,\;\beta ,\;\gamma $ are the geometric means between $ca,\;ab;\;ab,\;bc;\;bc,\;ca$ respectively where $a,\;b,\;c$ are in A.P., then ${\alpha ^2},\;{\beta ^2},\;{\gamma ^2}$ are in
  • ✓
    $A.P.$
  • B
    $H.P.$
  • C
    $G.P.$
  • D
    None of the above
✓

Answer

Correct option: A.
$A.P.$
a
(a) By hypothesis, ${\alpha ^2} = {a^2}bc,\;{\beta ^2} = {b^2}ca,\;{\gamma ^2} = {c^2}ab$ and $2b = a + c$.

.Hence ${2^{n - 1}} > 100$ are in A.P.

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