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CBSE Class 10 Answered

If the ratio of the sum of first n terms of two A.P's is ( 7n + 1): (4n + 27), find the ratio of their m th terms.
Asked by malaysaha.80 | 05 Feb, 2019, 11:32: AM
answered-by-expert Expert Answer
L e t space S subscript n space a n d space S subscript n apostrophe end subscript space a r e space s u m space o f space f i r s t space n space t e r m s space o f space t w o space d i f f e r e n t space A. P s I t space i s space g i v e n space t h a t comma S subscript n over S subscript n apostrophe end subscript equals fraction numerator 7 n plus 1 over denominator 4 n plus 27 end fraction U sin g space t h e space f o r m u l a space f o r space s u m space o f space f i r s t space n space t e r m s space o f space a n space A. P. space w e space h a v e fraction numerator begin display style n over 2 end style open parentheses 2 a plus left parenthesis n minus 1 right parenthesis d close parentheses over denominator begin display style fraction numerator n apostrophe over denominator 2 end fraction end style open parentheses 2 a apostrophe plus left parenthesis n apostrophe minus 1 right parenthesis d apostrophe close parentheses end fraction equals fraction numerator 7 n plus 1 over denominator 4 n plus 27 end fraction rightwards double arrow fraction numerator begin display style 2 a plus left parenthesis n minus 1 right parenthesis d end style over denominator begin display style 2 a apostrophe plus left parenthesis n apostrophe minus 1 right parenthesis d apostrophe end style end fraction equals fraction numerator 7 n plus 1 over denominator 4 n plus 27 end fraction rightwards double arrow fraction numerator begin display style a plus fraction numerator left parenthesis n minus 1 right parenthesis over denominator 2 end fraction d end style over denominator begin display style a apostrophe plus fraction numerator left parenthesis n apostrophe minus 1 right parenthesis over denominator 2 end fraction d apostrophe end style end fraction equals fraction numerator 7 n plus 1 over denominator 4 n plus 27 end fraction space............ space left parenthesis i right parenthesis N o w comma space m t h space t e r m space o f space a n space A. P. space i s space g i v e n space a s space a plus left parenthesis m minus 1 right parenthesis d S o comma space r a t i o space o f space m t h space t e r m s space o f space t h e space t w o space A. P s space i s colon t subscript m over t subscript m apostrophe end subscript equals fraction numerator a plus left parenthesis m minus 1 right parenthesis d over denominator a apostrophe plus left parenthesis m apostrophe minus 1 right parenthesis d apostrophe end fraction R e p l a c i n g space fraction numerator n minus 1 over denominator 2 end fraction space b y space m minus 1 space a n d space fraction numerator n apostrophe minus 1 over denominator 2 end fraction space b y space m apostrophe minus 1 space i n space left parenthesis i right parenthesis comma space w e space g e t n equals 2 left parenthesis m minus 1 right parenthesis plus 1 space a n d space n apostrophe equals 2 left parenthesis m apostrophe minus 1 right parenthesis d apostrophe rightwards double arrow t subscript m over t subscript m apostrophe end subscript equals fraction numerator 7 left parenthesis 2 left parenthesis m minus 1 right parenthesis plus 1 right parenthesis plus 1 over denominator 4 left parenthesis 2 left parenthesis m minus 1 right parenthesis plus 1 right parenthesis plus 27 end fraction equals fraction numerator 7 left parenthesis 2 m minus 1 right parenthesis plus 1 over denominator 4 left parenthesis 2 m minus 1 right parenthesis plus 27 end fraction equals fraction numerator 14 m minus 6 over denominator 8 m plus 23 end fraction
Answered by Renu Varma | 05 Feb, 2019, 12:22: PM

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