Question

Which term of AP $53,48,43...$ is the first negative term?

Answer 1

Find the first negative term.

Given AP is$53,48,43,\dots$
where, first term, $a=53$
common difference, $d=48-53=-5$
Let the first negative term in the AP be the nth term.
Then we must determine which value is the lowest.
$$\begin{gathered} a_n<0 \\ \Rightarrow a+(n-1)d<0 \\ \Rightarrow 53+(n-1)(-5)<0 \\ \Rightarrow 53-5(n-1)<0 \\ \Rightarrow 5(n-1)>53 \\ \Rightarrow \mathrm{n}-1>\frac{53}{5} \\ \Rightarrow n>1+\frac{53}{5} \\ \Rightarrow n>\frac{58}{5} \end{gathered}$$
Here, n will be the least natural number bigger than $\frac{58}{5}=11.65$, or $12$.
Therefore, 12th term Is the first negative term of the given AP.