Question

Which term of the AP, $19,18\frac{1}{5},17\frac{2}{5},...$ is the first negative term?

• A. $24$
• B. $25$
• C. $26$
• D. $23$

Answer 1

Answer: (B)

$25$

We must find the common difference of the A.P:-

Common difference $\left(d\right)=firstterm-secondterm$

$\begin{array}{c}=18\frac{1}{5}-19\\ =\frac{91}{5}-\frac{95}{5}\\ =\frac{-4}{5}\end{array}$

Hence,

the common difference is $\frac{-4}{5}or-0.8$

Now to estimate which term of this A.P will be negative let us assume

the $nth$ therm of A.P IS $0$.

Formula for the nth term of an A.P is $=a+\left(n-1\right)d$

then,

$\begin{array}{c}0=19+\left(n-1\right)\times -0.8\\ 0=19-0.8n+0.8\\ 0.8n=19.8\\ n=\frac{19.8}{0.8}\\ n=24.75\end{array}$

if the $24.75th$ term is $0$. Then surly $25th$ term of the

A.P will be negative.

Let us make sure, just in this case:

$\begin{array}{c}25thtermofanA.P=a+\left(n-1\right)d\\ =19+\left(25-1\right)\times -0.8\\ =19+\left(24\times -0.8\right)\\ =19+\left(-19.2\right)\\ =19-19.2\\ =-0.2\end{array}$

Thus, the $25th$ term of the progression is first negative term.

Hence,

option $B$ is correct answer.