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Sequences And Series

Question
CBSEENMA11015609
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Let a1, a2, a3, … be terms of an A.P. If fraction numerator straight a subscript 1 space plus straight a subscript 2 space plus......... straight a subscript straight p over denominator straight a subscript 1 space plus straight a subscript 2 space plus.......... straight a subscript straight q end fraction space equals space straight p squared over straight q squared comma space straight p not equal to straight q comma space then space straight a subscript 6 over straight a subscript 21 equals

  • 41/11

  • 7/2

  • 2/7

  • 11/47

Solution

D.

11/47

fraction numerator begin display style straight p over 2 open square brackets 2 straight a subscript 1 space plus left parenthesis straight p minus 1 right parenthesis straight d close square brackets end style over denominator begin display style straight q over 2 open square brackets 2 straight a subscript 1 space plus left parenthesis straight q minus 1 right parenthesis straight d close square brackets end style end fraction space equals space straight p squared over straight q squared rightwards double arrow space fraction numerator 2 straight a subscript 1 space plus left parenthesis straight p minus 1 right parenthesis straight d over denominator 2 straight a subscript 1 space plus left parenthesis straight q minus 1 right parenthesis straight d end fraction space equals straight p over straight q fraction numerator straight a subscript 1 space plus space open parentheses begin display style fraction numerator straight p minus 1 over denominator 2 end fraction end style close parentheses over denominator straight a subscript 1 space plus open parentheses begin display style fraction numerator straight q minus 1 over denominator 2 end fraction end style close parentheses straight d end fraction space equals straight p over straight q For space straight a subscript 6 over straight a subscript 21 comma space straight p equals 11 comma space 1 space equals space 41 rightwards arrow space straight a subscript 6 over straight a subscript 21 space equals 11 over 41

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