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8. Sequences and Series
medium
If $a,\,b,\,c$ are in $G.P.$, then
A
$a({b^2} + {a^2}) = c({b^2} + {c^2})$
B
$a({b^2} + {c^2}) = c({a^2} + {b^2})$
C
${a^2}(b + c) = {c^2}(a + b)$
D
None of these
Solution
(b) If $a,\;b,\;c$ are in $G.P.$ Then ${b^2} = ac$
$ \Rightarrow $ ${b^2}(a – c) = ac(a – c)$
$ \Rightarrow $${b^2}a – {b^2}c = {a^2}c – a{c^2}$
$ \Rightarrow $ $a({b^2} + {c^2}) = c({a^2} + {b^2})$.
Trick : Put $a = 1,\;b = 2,\;c = 4$ and check the alternates.
Standard 11
Mathematics
