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  • State whether statement in True or False. Two sequences cannot be in both A.P. and G.P. together.

State whether statement in True or False.  Two sequences cannot be in both A.P. and G.P. together.

Answers (1)

Let the terms of A.P be a, \left( a+d \right) , \left( a+2d \right) , \ldots

Let the terms of G.P be  a,ar,ar^{2}

  \\ a+d=ar \\\\ a+2d=ar^{2} \\\\ r=\frac{a+2d}{a+d}=\frac{a+d}{a} \\\\ a^{2}+2ad=a^{2}+2ad+d^{2} \\\\ d^{2}=0 \\\\ r=\frac{a+2 \left( 0 \right) }{a+ \left( 0 \right) }=1 \\\\

So the terms of A.P and G.P are same   

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infoexpert21

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