From the question it is given that,
First term a =
![\[20\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f909910e2f598933c23989d90a7a4169_l3.png "Rendered by QuickLaTeX.com")
Common difference d =
![\[19{\scriptscriptstyle 1\!/\!{ }_4}\text{ }\text{ }20\text{ }=\text{ }77/4\text{ }\text{ }20\text{ }=\text{ }\left( 77\text{ }\text{ }80 \right)/4\text{ }=\text{ }-{\scriptscriptstyle 3\!/\!{ }_4}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0a3c6095edac90a662be79795289eedf_l3.png "Rendered by QuickLaTeX.com")
We know that, an = a + (n – 1)d
![\[\begin{array}{*{35}{l}} {{a}_{n}}~=\text{ }20\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)\text{ }\left( -{\scriptscriptstyle 3\!/\!{ }_4} \right) \\ {{a}_{n}}~=\text{ }20\text{ }\text{ }{\scriptscriptstyle 3\!/\!{ }_4}n\text{ }+\text{ }{\scriptscriptstyle 3\!/\!{ }_4} \\ {{a}_{n}}~=\text{ }20\text{ }+\text{ }{\scriptscriptstyle 3\!/\!{ }_4}\text{ }\text{ }{\scriptscriptstyle 3\!/\!{ }_4}n \\ {{a}_{n}}~=\text{ }\left( 80\text{ }+\text{ }3 \right)/4\text{ }\text{ }{\scriptscriptstyle 3\!/\!{ }_4}n \\ {{a}_{n}}~=\text{ }83/4\text{ }\text{ }{\scriptscriptstyle 3\!/\!{ }_4}n\text{ }<\text{ }0 \\ 83/4\text{ }<\text{ }{\scriptscriptstyle 3\!/\!{ }_4}n \\ 83\text{ }<\text{ }3n \\ 83/3\text{ }<\text{ }n \\ 28\text{ }<\text{ }n \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-00cae494576adb1c23408ed86da8325e_l3.png "Rendered by QuickLaTeX.com")
Therefore,
![\[{{28}^{th}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-97fabad5e0e9dbb7ce8cc6b039f438e4_l3.png "Rendered by QuickLaTeX.com")
is the first negative term.
Which term of the list of numbers
![\[\mathbf{20},\text{ }\mathbf{19}{\scriptscriptstyle 1\!/\!{ }_4},\text{ }\mathbf{18}{\scriptscriptstyle 1\!/\!{ }_2},\text{ }\mathbf{17}{\scriptscriptstyle 3\!/\!{ }_4},\text{ }\ldots \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9edef3ce91c7c8c31cec2e1c8801b2ad_l3.png "Rendered by QuickLaTeX.com")
From the question it is given that,
First term a =
Common difference d =
We know that, an = a + (n – 1)d
Therefore,
is the first negative term.