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| 1. |
Which term of the progression 19,181/5, |
| Answer» \xa0According to condition the given arithmetic progression is 19,18{tex}\\frac{1}{5}{/tex},17{tex}\\frac{2}{5}{/tex}.........(i)Here, T2\xa0- T1\xa0=\xa0{tex}\\frac { 91 } { 5 } - 19 = \\frac { 91 - 95 } { 5 } = - \\frac { 4 } { 5 }{/tex}T3\xa0- T2\xa0=\xa0{tex}\\frac { 87 } { 5 } - \\frac { 91 } { 5 } = - \\frac { 4 } { 5 }{/tex}Therefore, (i) is an arithmetic progression with a = 19, d =\xa0{tex}-\\frac{4}{5}{/tex}Suppose, the nth term of the given arithmetic progression be the first negative term. Then, nth term < 0.{tex}\\Rightarrow{/tex}\xa0Tn\xa0< 0\xa0{tex}\\Rightarrow{/tex}\xa0[ 19 + (n - 1){tex}\\left( - \\frac { 4 } { 5 } \\right){/tex}] < 0{tex}\\Rightarrow{/tex}\xa0(99 - 4n) < 0\xa0{tex}\\Rightarrow{/tex}\xa04n > 99\xa0{tex}\\Rightarrow{/tex}\xa0n >\xa0{tex}24 \\frac { 3 } { 4 }{/tex}.{tex}\\therefore{/tex}\xa0n = 25,i.e., 25th is the first negative term in the given AP. | |