sir, please explain me the 1(ii) of exercise no. 5.1 in NCERT BOOK. What is the difference between A.P and G.P ?
 

Asked by mrinalini mrinalini | 22nd Oct, 2014, 06:28: PM

Expert Answer:

T h e space a m o u n t space o f space a i r space p r e s e n t space i n space a space c y l i n d e r space w h e n space a space v a c u u m space p u m p space r e m o v e s space 1 fourth space o f space t h e space a i r space r e m a i n i n g space i n space t h e space c y l i n d e r space a t space a space t i m e. S o l u t i o n : space L e t space t h e space a m o u n t space o f space a i r space b e space x space c m cubed A m o u n t space o f space a i r space l e f t space a f t e r space r e m o v i n g space 1 fourth o f space a i r space i n space c y l i n d e r space equals x minus space x over 4 equals fraction numerator 3 x over denominator 4 end fraction space c m cubed A m o u n t space o f space a i r space l e f t space a f t e r space s e c o n d space r e m o m v a l equals fraction numerator 3 x over denominator 4 end fraction minus 1 fourth open parentheses fraction numerator 3 x over denominator 4 end fraction close parentheses equals fraction numerator 12 x minus 3 x over denominator 16 end fraction equals fraction numerator 9 x over denominator 16 end fraction c m cubed A m o u n t space o f space a i r space a f t e r space t h i r d space r e m o v a l equals fraction numerator 9 x over denominator 16 end fraction minus 1 fourth open parentheses fraction numerator 9 x over denominator 16 end fraction close parentheses equals fraction numerator 27 x over denominator 64 end fraction c m cubed L e t space t subscript 1 equals fraction numerator 3 x over denominator 4 end fraction comma space t subscript 2 equals fraction numerator 9 x over denominator 16 end fraction comma space t subscript 3 equals fraction numerator 27 x over denominator 64 end fraction because t subscript 2 minus t subscript 1 not equal to t subscript 3 minus t subscript 2 therefore T h e space s e r i e s space i s space n o t space i n space A P A P space i s space A i r t h m e t i c space P r o g r e s s i o n comma space G P space i s space G e o m e t r r i c space P r o g r e s s i o n. I f space i n space a space s e r i e s comma space t h e space d i f f e r e n c e space b e t w e e n space t w o space c o n s e c u t i v e space t e r m s space i s space s a m e space t h r o u g h o u t space t h e space s e r i e s comma space t h e n space t h e space s e r i e s space i s space a n A P. I f space i n space a space s e r i e s comma space t h e space r a t i o space o f space t w o space c o n s e c u t i v e space t e r m s space i s space s a m e space t h r o u g h o u t space t h e space s e r i e s. space t h e n space t h e space s e r i e s space i s space a space G P F o r space e x a m p l e comma space 1 comma 3 comma 5 comma 7 comma.... space i s space a n space A P. 2 comma 4 comma 8 comma 16 comma..... i s space a space G P

Answered by Prasenjit Paul | 25th Oct, 2014, 12:50: AM