Question

Find the ${20}^{th}$ term of an A.P. whose $5^{th}$ term is $15$ and the sum of its $3^{rd}$ and $8^{th}$ terms is $34$.

Answer 1

$t_5=t_5$ and $t_3+t_8=34$
$\Rightarrow a+4d=15$ ...(i)
and $(a+2d)+(a+7d)=34$
$\Rightarrow 2a+9d=34$ ...(ii)
(i) and (ii) gives $d=4$ and $a=-1$
$\therefore t_{20}=a+19d=-1+19\times 4=75$