Answer:
Given, A.P is \[20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4},\]???. \[=20,\frac{77}{4},\frac{37}{2},\frac{71}{4},\]?? Here, \[a=20,d=\frac{77}{4}-20=\frac{77-80}{4}=\frac{-3}{4}\] Let \[{{a}_{n}}\] is first negative term \[\Rightarrow \] \[{{a}_{n}}+(n-1)d<0\] \[\Rightarrow \] \[20+(n-1)\left( -\frac{3}{4} \right)<0\] \[\Rightarrow \] \[20-\frac{3}{4}n+\frac{3}{4}<0\] \[\Rightarrow \] \[20+\frac{3}{4}<\frac{3}{4}n\] \[\Rightarrow \] \[\frac{83}{4}<\frac{3}{4}n\] \[\Rightarrow \] \[n>\frac{83}{4}\times \frac{4}{3}\] \[\Rightarrow \] \[n>\frac{83}{4}=27.66\] 28th term will be first negative term of given A.P.
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