Question

Which term of the AP $24,21,18,15,.....$ is first negative terms?

Answer 1

Here $a_1=24,a_2=21$

Common difference $d=a_2-a_1=21-24=-3$

$\Rightarrow$$a_n=a_1+(n-1)d{n}^{th}$ term formula

We first find the value of $n$ for which the value of $n$ is zero

The next integer value of that $n$ will be the term of first negative number

$\Rightarrow$$a_n=a_1+(n-1)d$

$\Rightarrow$$0=24+(n-1)(-3)$

$\Rightarrow$$-24=(n-1)-3$

$\Rightarrow$$8=n-1$

$\Rightarrow$$n=9$

Hence, ${10}^{th}$ term will be the first negative term of given AP

$a_{10}=a_1+(n-1)d=24+9\times (-3)=-3$