Question

Find the $8$th term from the end of the A.P. $7,10,13,.......,184$.

Answer 1

Given sequence is $7,10,13,...,184$

The first term is $a=7$

The common difference is $d=10-7=3$

The last term is $184$

we know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=184$

$⟹7+(n-1)3=184$

$⟹3n-3=177$

$⟹3n=180$

$⟹n=\frac{180}{3}=60$

Therefore, there are $60$ terms in the sequence.

Hence, the $8^{th}$ term from the end is $60-8+1={53}^{rd}$ term from the beginning.

Therefore, the ${53}^{rd}$ term is $a+(53-1)d=7+52\left(3\right)=163$