Question

Which term of the arithmetic progression $8,14,20,\mathrm{26.........}$ will be $144$ more than ${23}^{rd}$ term?

Answer 1

${23}^{rd}$ term $=8+(23-1)\times 6=140$

If required term is $144$ more than ${23}^{rd}$ term, then term $=144+140=284$

Thus $284=8+(n-1)\times 6$

$\Rightarrow 276=6(n-1)$

$\Rightarrow n-1=46$

$\Rightarrow n=47$

Therefore, ${47}^{th}$ term of the given series will be $144$ more than ${23}^{rd}$ term.