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

Solution:

In the given problem, we need to find the 8th term from the end for the given A.P.

We have the A.P as 7, 10, 13 …184

Here, to find the 8th term from the end let us first find the total number of terms. Let us take the total number of terms as n.

So,

First term (a) = 7

Last term (an) = 184

Common difference $(d)=10-7=3$

Now, as we know,

$a_{n}=a+(n-1) d$

So, for the last term,

$184=7+(n-1) 3$

$184=7+3 n-3$

 

$184=4+3 n$

$184-4=3 n$

Further simplifying,

$180=3 n$

$n=\frac{180}{3}$

$n=60$

So, the 8th term from the end means the 53rd term from the beginning.

So, for the 53rd term (n = 53)

$a_{53}=7+(53-1) 3$

$=7+(52) 3$

$=7+156$

 

$=163$

Therefore, the $8^{\text {th }}$ term from the end of the given A.P. is 163 .