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  4. A sequence of three real numbers form an A.P. and the first term is 25. If 20 is subtracted from second term and 4 subtracted from third term, the resulting numbers form a G.P., then maximum value of second term of G.P. will be

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Q. A sequence of three real numbers form an A.P. and the first term is 25. If 20 is subtracted from second term and 4 subtracted from third term, the resulting numbers form a G.P., then maximum value of second term of G.P. will be

Sequences and Series

Solution:

$\text { Let term be } 25,25+ d , 25+2 d $
$\therefore 25,5+ d , 21+2 d \Rightarrow G . P . $
$\therefore(5+ d )^2=25(21+2 d ) $
$\Rightarrow d ^2-40 d -500=0 \Rightarrow( d -50)( d +10)=0$
$\Rightarrow d =50 \text { or } d =-10$
$\therefore \text { maximum value of second term of G.P. }=5+50=55$