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| 1. |
which term of the progression 20,19¼,18½,17¾......is the first negative term? |
| Answer» Given, a = 20 and d =\xa0{tex}-\\frac 34{/tex}Let the nth term be first negative term{tex}a + (n - 1)d {/tex}< 0{tex}\\therefore{/tex}\xa0{tex}20 + ( n - 1 ){/tex} ( - {tex}\\frac 34{/tex}\xa0) < 0\xa020- {tex}\\frac 34{/tex}n + {tex}\\frac 34{/tex}\xa0< 0- {tex}\\frac 34{/tex}n + {tex}\\frac {83}4{/tex}\xa0< 0{tex}\\frac {83}4{/tex}\xa0< {tex}\\frac 34{/tex}n3n > 83n >\xa0{tex}\\frac { 83 } { 3 } = 27 \\frac { 2 } { 3 }{/tex}Hence 28th term is first negative. | |