Question

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

Answer 1

For the given A.P.,

First term$\left(a\right)=3$

Last term$\left(t_n\right)=253$

Common Difference$\left(d\right)=8-3=5$

$\because t_n=a+(n-1)d$

$\Rightarrow 253=3+(n-1)\times 5$

$\Rightarrow 253-3=(n-1)\times 5$

$\Rightarrow 250÷5=n-1$

$\Rightarrow 50+1=n$

$\therefore n=51$

In 51 terms, ${20}^{th}$ term from the last term will be $51-20+1={32}^{th}$

$\therefore t_{32}=a+(32-1)d=3+31\times 5=3+155=158$