Q

Asked by araima2001 | 3rd Sep, 2016, 08:04: AM

Expert Answer:

begin mathsize 16px style The space ratio space of space the space sum space of space straight n space terms space of space two space AP apostrophe straight s space equals space fraction numerator 7 straight n plus 1 over denominator 4 straight n plus 27 end fraction
We space know space that comma space sum space of space straight n space term space of space an space AP space equals space straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d right square bracket
So comma space fraction numerator straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d right square bracket over denominator straight n over 2 left square bracket 2 straight a apostrophe space plus space left parenthesis straight n minus 1 right parenthesis straight d apostrophe right square bracket end fraction equals space fraction numerator 7 straight n plus 1 over denominator 4 straight n plus 27 end fraction
rightwards double arrow fraction numerator 2 straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d over denominator 2 straight a apostrophe space plus space left parenthesis straight n minus 1 right parenthesis straight d apostrophe end fraction equals space fraction numerator 7 straight n plus 1 over denominator 4 straight n plus 27 end fraction
Now comma space let space the space ratio space of space the space 11 th space term space of space the space AP apostrophe straight s space equals space straight a subscript 11 colon space straight a apostrophe subscript 11
We space know space that space straight a subscript straight n equals straight a plus left parenthesis straight n minus 1 right parenthesis straight d
So comma space fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals space fraction numerator straight a plus left parenthesis 11 minus 1 right parenthesis straight d over denominator straight a apostrophe plus left parenthesis 11 minus 1 right parenthesis straight d apostrophe end fraction
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals space fraction numerator 2 straight a plus 2 left parenthesis 11 minus 1 right parenthesis straight d over denominator 2 straight a apostrophe plus 2 left parenthesis 11 minus 1 right parenthesis straight d apostrophe end fraction.... left parenthesis Mutiplying space by space 2 right parenthesis
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals space fraction numerator 2 straight a plus left parenthesis 22 minus 2 right parenthesis straight d over denominator 2 straight a apostrophe plus left parenthesis 22 minus 2 right parenthesis straight d apostrophe end fraction
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals space fraction numerator 2 straight a plus left square bracket 21 minus 1 right square bracket straight d over denominator 2 straight a apostrophe plus left square bracket 21 minus 1 right square bracket straight d apostrophe end fraction
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals space fraction numerator straight S subscript 21 over denominator straight S apostrophe subscript 21 end fraction
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals fraction numerator 7 left parenthesis 21 right parenthesis plus 1 over denominator 4 left parenthesis 21 right parenthesis plus 27 end fraction
rightwards double arrow fraction numerator straight a subscript 11 over denominator straight a apostrophe subscript 11 end fraction equals 148 over 111
So comma space the space ratio space of space the space 11 th space terms space of space the space two space APs space is space 148 colon 111.

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Answered by Rebecca Fernandes | 3rd Sep, 2016, 10:39: AM

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