From the question,
The first term a =
![\[53\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-20dc1f87d3357ffe4465c46ecd7ffc17_l3.png "Rendered by QuickLaTeX.com")
Then, difference d
![\[\begin{array}{*{35}{l}} =\text{ }48\text{ }\text{ }53\text{ }=\text{ }-5 \\ =\text{ }43\text{ }\text{ }48\text{ }=\text{ }-5 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-eb225281fd47c798c74e18fd3d5a5d25_l3.png "Rendered by QuickLaTeX.com")
Therefore, common difference d =
![\[-5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e1e14d2d0bc643096abb417cd5c45865_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} {{T}_{n}}~=\text{ }a\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)d \\ =\text{ }53\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)\left( -5 \right) \\ =\text{ }53\text{ }\text{ }5n\text{ }+\text{ }5 \\ =\text{ }58\text{ }\text{ }5n \\ 5n\text{ }=\text{ }58 \\ n=\text{ }58/5 \\ n\text{ }=\text{ }11.6\text{ }\approx \text{ }12 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6b339c278304d2ba432c721d6b22ede4_l3.png "Rendered by QuickLaTeX.com")
Therefore,
![\[{{12}^{th}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a6c9088a52c32f5016b8782b109e56df_l3.png "Rendered by QuickLaTeX.com")
term is the first negative term of the A.P.
![\[\mathbf{53},\text{ }\mathbf{48},\text{ }\mathbf{43},\ldots \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-03ea2d2c0b9d00d149b1de331d89a638_l3.png "Rendered by QuickLaTeX.com")
Which term of the A.P.
From the question,
The first term a =
Then, difference d
Therefore, common difference d =
Therefore,
term is the first negative term of the A.P.