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8. Sequences and Series
medium
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
$A.P.$
B
$H.P.$
C
$G.P.$
D
None of the above
Solution
(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.
Standard 11
Mathematics
