Question

Find the $8^{th}$ term from the end of the AP $7,10,13,...............,184.$

Answer 1

Solution:-

$A.P.\to 7,10,13,.............,184$

First term, $\left(a\right)=7$

common difference, $\left(d\right)=a_2-a_1=10-7=3\{\because d={(n+1)}^{th}term-n^{th}term\}$

As we have to find $8^{th}$ term from the end,

New A.P. $\to 184,181,178,........................7$

First term of new A.P. $\left(a^{\prime }\right)=184$

common difference of new A.P., $\left(d^{\prime }\right)=a_2-a_1=181-184=-3$

$\therefore a_8=a+7d\{a_n=a+(n-1)d\}$

$\Rightarrow a_8=184+(7\times -3)$

$\Rightarrow a_8=184-21=163$

Hence, $8^{th}$ term from the end of the A.P. $7,10,13,.............,184$ is $163$.