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JEE Class main Answered

Sir pls solve the following.
question image
Asked by rsudipto | 28 Dec, 2018, 07:52: PM
answered-by-expert Expert Answer
Reciprocals of p-th, q-th and r-th terms are in A.P.
 
Let a be the first term and d is the common difference of A.P.
 
begin mathsize 12px style t subscript p space equals space a space plus space left parenthesis p minus 1 right parenthesis d space equals space 1 over u space.............. left parenthesis 1 right parenthesis
t subscript q space equals space a space plus left parenthesis q minus 1 right parenthesis d space equals space 1 over v space................ left parenthesis 2 right parenthesis
t subscript r space equals space a plus space left parenthesis r minus 1 right parenthesis d space equals space 1 over w space............... left parenthesis 3 right parenthesis
e q n. left parenthesis 1 right parenthesis space minus space e q n left parenthesis 2 right parenthesis space g i v e s comma space space open parentheses p minus q close parentheses d space equals space 1 over u minus 1 over v space space o r space space space left parenthesis p minus q right parenthesis u v space equals space 1 over d left parenthesis v minus u right parenthesis space........... left parenthesis 4 right parenthesis
e q n. left parenthesis 2 right parenthesis space minus space e q n. left parenthesis 3 right parenthesis space g i v e s comma space open parentheses q minus r close parentheses d space equals space 1 over v minus 1 over w space space o r space space space left parenthesis q minus r right parenthesis v w space equals space 1 over d left parenthesis w minus v right parenthesis space............. left parenthesis 5 right parenthesis
e q n. left parenthesis 3 right parenthesis space minus space e q n. left parenthesis 1 right parenthesis space g i v e s comma space left parenthesis r minus p right parenthesis d space equals space 1 over w minus 1 over u space space o r space space space left parenthesis r minus p right parenthesis w u space equals 1 over d open parentheses u minus w close parentheses space............. left parenthesis 6 right parenthesis
b y space a d d i n g space e q n. left parenthesis 4 right parenthesis comma left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space g e t comma space space space space open parentheses p minus q close parentheses u v space plus space open parentheses q minus r close parentheses v w space plus space open parentheses r minus p close parentheses w u space equals space 0 end style
Answered by Thiyagarajan K | 30 Dec, 2018, 07:30: PM

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