Question

Which term of the A.P. $53,48,43,\dots$ is the first negative term?

Answer 1

From the question,

The first term $a=53$

Then, difference $d=48-53=-5$

$=43-48=-5$

Therefore, common difference $d=-5$

$\begin{array}{cc}{T}_n& =a+(n-1)d\\ & =53+(n-1)(-5)\\ & =53-5n+5\\ & =58-5n\\ 5n& =58\\ n& =58/5\\ n& =11.6\approx 12\end{array}$

Therefore, ${12}^{\text{th}}$ term is the first negative term of the A.P. $53,48,43,\dots$