Question
Sun March 08, 2015 By: Surajsubedi14

Find four numbers forming a geomatric progression in which the third term is greater than the first term by 9 and the second term is greater than the fourth term by 18.

Expert Reply
Rashmi Khot
Sun March 08, 2015

begin mathsize 18px style L e t space a space b e space t h e space f i r s t space t e r m space a n d space r space b e space t h e space c o m m o n space r a t i o space o f space t h e space G. P. T h u s comma a subscript 1 equals a comma space a subscript 2 equals a r comma space a subscript 3 equals a r squared comma space a subscript 4 equals a r cubed A c c o r d i n g space t o space g i v e n space i n f o r m a t i o n comma space w e space h a v e a subscript 3 equals a subscript 1 plus 9 space space space rightwards double arrow a r squared equals a plus 9 space space rightwards double arrow a left parenthesis r squared minus 1 right parenthesis equals 9 space.... left parenthesis 1 right parenthesis A l s o comma a subscript 2 equals a subscript 4 plus 18 space space space rightwards double arrow a r equals a r cubed plus 18 space space space rightwards double arrow a r left parenthesis 1 minus r squared right parenthesis equals 18 space space space.... left parenthesis 2 right parenthesis  end style

begin mathsize 16px style D i v i d i n g space left parenthesis 2 right parenthesis space b y space left parenthesis 3 right parenthesis comma space w e space g e t fraction numerator a r left parenthesis 1 minus r squared right parenthesis over denominator a left parenthesis r squared minus 1 right parenthesis end fraction equals 18 over 9 rightwards double arrow negative r equals 2 rightwards double arrow r equals negative 2 S u b s t i t u t n g space r space equals space minus 2 space i n space a r squared equals a plus 9 comma space w e space g e t 4 a equals a plus 9 rightwards double arrow 3 a equals 9 rightwards double arrow a equals 3 T h u s comma space t h e space f o u r space n u m b e r s space i n space G. P. space a r e a space equals space 3 a r equals 3 left parenthesis negative 2 right parenthesis equals negative 6 a r squared equals 3 left parenthesis negative 2 right parenthesis squared equals 3 left parenthesis 4 right parenthesis equals 12 space a n a r cubed equals 3 left parenthesis negative 2 right parenthesis cubed equals 3 left parenthesis negative 8 right parenthesis equals negative 24 end style
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