If 77th term of Ap=1/9 and9th=1/7 find 63th term

1.	If 77th term of Ap=1/9 and9th=1/7 find 63th term
Answer» Let a be the first term and d be the common difference of the given AP. Then,{tex}T _ { 7 } = \\frac { 1 } { 9 } \\Rightarrow a + 6 d = \\frac { 1 } { 9 }{/tex}\xa0...(i){tex}T _ { 9 } = \\frac { 1 } { 7 } \\Rightarrow a + 8 d = \\frac { 1 } { 7 }{/tex}\xa0...(i)On subtracting (i) from (ii), we get{tex}2 d = \\left( \\frac { 1 } { 7 } - \\frac { 1 } { 9 } \\right) = \\frac { 2 } { 63 } \\Rightarrow d = \\left( \\frac { 1 } { 2 } \\times \\frac { 2 } { 63 } \\right) = \\frac { 1 } { 63 }.{/tex}Putting d =\xa0{tex}\\frac { 1 } { 63 }{/tex}in (i), we get{tex}a + \\left( 6 \\times \\frac { 1 } { 63 } \\right) = \\frac { 1 } { 9 } \\Rightarrow a + \\frac { 2 } { 21 } = \\frac { 1 } { 9 } \\Rightarrow a = \\left( \\frac { 1 } { 9 } - \\frac { 2 } { 21 } \\right) = \\left( \\frac { 7 - 6 } { 63 } \\right) = \\frac { 1 } { 63 }.{/tex}Thus, a =\xa0{tex}\\frac { 1 } { 63 }{/tex}\xa0and d =\xa0{tex}\\frac { 1 } { 63 }.{/tex}{tex}\\therefore{/tex}\xa0T63 = a + (63-1)d = (a + 62d){tex}= \\left( \\frac { 1 } { 63 } + 62 \\times \\frac { 1 } { 63 } \\right) = \\left( \\frac { 1 } { 63 } + \\frac { 62 } { 63 } \\right) = 1.{/tex}Hence, 63rd term of the given AP is 1.

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