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The sum of n terms of two A.P are in the ratio (3n+8):(7n+15).Find the ratio of there 12th terms.
 
[why is n=23 towards the ending of the solution and how do we find n in the question?] 

Asked by Deebu 29th November 2014, 2:03 PM
Answered by Expert
Answer:
G i v e n space t h a t space t h e space s u m space o f space n space t e r m s space o f space t w o space A P space a r e space i n space t h e space r a t i o space left parenthesis 3 n plus 8 right parenthesis : left parenthesis 7 n plus 15 right parenthesis. L e t space a subscript 1 space a n d space d subscript 1 space b e space t h e space i n t i a l space t e r m space a n d space t h e space c o m m o n space d i f f e r e n c e space o f space f i r s t space A P A n d space l e t space a subscript 2 space a n d space d subscript 2 space b e space t h e space i n i t i a l space t e r m space a n d space t h e space c o m m o n space d i f f e r e n c e space o f space s e c o n d space A P. F r o m space t h e space g i v e n space s t a t e m e n t comma space w e space h a v e fraction numerator 2 a subscript 1 plus open parentheses n minus 1 close parentheses d subscript 1 over denominator 2 a subscript 2 plus open parentheses n minus 1 close parentheses d subscript 2 end fraction equals fraction numerator 3 n plus 8 over denominator 7 n plus 15 end fraction rightwards double arrow fraction numerator begin display style fraction numerator 2 a subscript 1 plus open parentheses n minus 1 close parentheses d subscript 1 over denominator 2 end fraction end style over denominator begin display style fraction numerator 2 a subscript 2 plus open parentheses n minus 1 close parentheses d subscript 2 over denominator 2 end fraction end style end fraction equals fraction numerator 3 n plus 8 over denominator 7 n plus 15 end fraction rightwards double arrow fraction numerator a subscript 1 plus begin display style fraction numerator open parentheses n minus 1 close parentheses over denominator 2 end fraction end style d subscript 1 over denominator a subscript 2 plus begin display style fraction numerator open parentheses n minus 1 close parentheses over denominator 2 end fraction end style d subscript 2 end fraction equals fraction numerator 3 n plus 8 over denominator 7 n plus 15 end fraction.... left parenthesis 1 right parenthesis W h e n space fraction numerator open parentheses n minus 1 close parentheses over denominator 2 end fraction equals 11 comma space w e space h a v e comma space n minus 1 equals 22 rightwards double arrow n equals 22 plus 1 equals 23 S u b s t i t u t i n g space fraction numerator open parentheses n minus 1 close parentheses over denominator 2 end fraction equals 11 space a n d space n equals 23 space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e fraction numerator a subscript 1 plus begin display style 11 end style d subscript 1 over denominator a subscript 2 plus begin display style 11 end style d subscript 2 end fraction equals fraction numerator 3 cross times 23 plus 8 over denominator 7 cross times 23 plus 15 end fraction rightwards double arrow m over n equals 77 over 176 T h u s comma space t h e space r a t i o space o f space t h e space 12 space t e r m s space o f space t w o space A P s space i s space 77 : 176
Answered by Expert 30th November 2014, 12:17 PM
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