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Home  >>  CBSE XI  >>  Math  >>  Sequences and Series
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If $a,b,c,d$ are in G.P. then show that $(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P.

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  • If $x,y,z$ are in G.P. then $y^2=xy$
Given that $a,b,c,d$ are in G.P.
Let $a,b,c,d$ represent first four terms of a G.P.
To show three terms $x,y,z$ are in G.P. we have to show that $y^2=xy$
$\therefore$ To show that $(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P we have
to show that $(b^n+c^n)^2=(a^n+b^n). (c^n+d^n)$
Step 2
$(a^n+b^n). (c^n+d^n)=a^n(1+r^n)a^n.r^{2n}(1+r^n)$
$\therefore$ From (i) and (ii) $ (b^n+c^n)^2=(a^n+b^n). (c^n+d^n)$
$\Rightarrow\:(a^n+b^n),(b^n+c^n),(c^n+d^n)$ are in G.P.
Hence proved.
answered Mar 31, 2014 by rvidyagovindarajan_1

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