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  • The sum of the first three term of GP .is S and their product is 27 . then all such S lie in :

The sum of the first three term of GP .is S and their product is 27 . then all such S lie in :

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Solution: Let a is first term and r is the common ratio

Now,

\ a/r imes a imes ar=27\ \Rightarrow a=3\\Rightarrow a/r+a+ar=S\ \Rightarrow 1/r+1+r=S/3\ \Rightarrow r+1/r=S/3-1

\(r+1/r)geq 2;or;(r+1/r)leq -2\ \Rightarrow S/3geqslant 3;or S/3leq -1\ \Rightarrow Sgeq 9;or;Sleq -1

 

 
Posted by

Deependra Verma

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