Question

Find the $20$th term from the last term of the AP $:3,8,13,...,253.$

Answer 1

$3,8,13,.....,253$
$d=8-3=5$.

Writing this A.P. in reverse order
$253,248,243,\dots ,13,8,5$

Now, for the new A.P., we have

$a=253$

$d=248-253$

$d=-5$

We want to find $20$th term, so $n=20$

By using nth term $t_n=a+(n-1)d$ we have

$a_{20}=253+(20-1)(-5)$

$\Rightarrow 1_{20}=253+\left(19\right)(-5)$

$\Rightarrow a_{20}=253-95=158$

${20}^{th}$ term from the last term $=158$.