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CBSE Class 10 Answered

THe ratio of the sum of first n terms of Two APs is (4n+2):(3n+47).Find the ratio of their 9th terms.
 
Asked by neeraj | 21 Jan, 2016, 07:41: PM
answered-by-expert Expert Answer
Let space straight a comma straight b space be space the space first space terms space and space straight d comma straight e space be space the space common space differences space of space the space two space given space AP apostrophe straight s. Then space sum space to space their space straight n space terms space is space given space by comma straight S subscript straight n equals end subscript straight n over 2 open curly brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close curly brackets straight S apostrophe subscript straight n equals end subscript straight n over 2 open curly brackets 2 straight b plus open parentheses straight n minus 1 close parentheses straight e close curly brackets fraction numerator straight n over 2 open curly brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close curly brackets over denominator straight n over 2 open curly brackets 2 straight b plus open parentheses straight n minus 1 close parentheses straight e close curly brackets end fraction equals fraction numerator 4 straight n plus 2 over denominator 3 straight n plus 47 end fraction fraction numerator open curly brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close curly brackets over denominator open curly brackets 2 straight b plus open parentheses straight n minus 1 close parentheses straight e close curly brackets end fraction equals fraction numerator 4 straight n plus 2 over denominator 3 straight n plus 47 end fraction put space straight n equals left parenthesis 2 left parenthesis 9 right parenthesis minus 1 right parenthesis fraction numerator open curly brackets 2 straight a plus open parentheses 2 left parenthesis 9 right parenthesis minus 1 minus 1 close parentheses straight d close curly brackets over denominator open curly brackets 2 straight b plus open parentheses 2 left parenthesis 9 right parenthesis minus 1 minus 1 close parentheses straight e close curly brackets end fraction equals fraction numerator 4 left parenthesis 2 left parenthesis 9 right parenthesis minus 1 right parenthesis plus 2 over denominator 3 left parenthesis 2 left parenthesis 9 right parenthesis minus 1 right parenthesis plus 47 end fraction fraction numerator open curly brackets straight a plus 8 straight d close curly brackets over denominator open curly brackets straight b plus 8 straight e close curly brackets end fraction equals 70 over 98 equals 5 over 7 Ratio space of space 9 th space terms space is space 5 colon 7
Answered by Vijaykumar Wani | 22 Jan, 2016, 11:16: AM

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