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CBSE Class 10 Answered

Two arithmetic progressions have the same numbers of term. The ratio of the last term of the first progression to the first term of the second progression is equal to the ratio of the last term of second progression to the first term of the first progression and is equal to 4. The ratio of the sum of n terms of the first progression to the sum of n terms of second progression is equal to 2. Find the ratio of their common difference and ratio of their nth term
Asked by acv27joy | 17 Dec, 2018, 03:49: PM
answered-by-expert Expert Answer
Let a and d are first term and common difference of first A.P
Let b and e are first term and common difference of second A.P
 
Then as per the given information, we have,
 
begin mathsize 12px style fraction numerator a plus left parenthesis n minus 1 right parenthesis d over denominator b end fraction space equals space fraction numerator b plus left parenthesis n minus 1 right parenthesis e over denominator a end fraction space equals space 4 space.......... left parenthesis 1 right parenthesis h e n c e comma space space space a plus left parenthesis n minus 1 right parenthesis d space equals space 4 b space space................ left parenthesis 2 right parenthesis b plus left parenthesis n minus 1 right parenthesis e space equals space 4 a space............... left parenthesis 3 right parenthesis a l s o space f r o m space t h e space r a t i o space o f space t h e i r space s u m comma space fraction numerator 2 a plus left parenthesis n minus 1 right parenthesis d over denominator 2 b plus left parenthesis n minus 1 right parenthesis e space end fraction space equals space 2 space........ left parenthesis 4 right parenthesis U sin g space e q n. left parenthesis 2 right parenthesis space a n d space e q n. left parenthesis 3 right parenthesis space i n space e q n. left parenthesis 4 right parenthesis comma space fraction numerator a plus 4 b over denominator b plus 4 a end fraction space equals space 2 space.......... left parenthesis 5 right parenthesis h e n c e space space a plus 4 b space equals space 2 b space plus space 8 a space o r space a over b equals 2 over 7............ left parenthesis 6 right parenthesis l e t space u s space e l i m i n a t e space a space i n space e q n s. left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis space u sin g space e q n. left parenthesis 6 right parenthesis 2 over 7 b space plus open parentheses n minus 1 close parentheses d space equals space 4 b space space o r space space left parenthesis n minus 1 right parenthesis d space equals 26 over 7 b space space space............ left parenthesis 7 right parenthesis b plus left parenthesis n minus 1 right parenthesis e space equals space 8 over 7 b space space space space o r space space space left parenthesis n minus 1 right parenthesis e space equals space 1 over 7 b space.............. left parenthesis 8 right parenthesis f r o m space left parenthesis 7 right parenthesis space a n d space left parenthesis 8 right parenthesis comma space w e space h a v e space d over e space equals space 26 space............. left parenthesis 9 right parenthesis end style
From Eqn.(6), we have, ratio of first terms = 2/7  and from eqn.(9), ratio of common difference = 26
Answered by Thiyagarajan K | 19 Dec, 2018, 02:50: PM

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