Question

If $73$ is the $n^{th}$ term of the arithmetic progression $3,8,13,18\dots .$, then $‘n’$ is:

Answer 1

Find the value of $‘n’$

Given, $3,8,13,18\dots .$, is in A.P. and the $n^{th}$ term is $73$.

The formula for $n^{th}$ term of an A.P. is given by, $a_n=a+(n-1)d$ where $a$ is the first term and $d$ is the common difference.

Here, $a=3$ and $d=8–3=5$.

So, putting the above values of $a$ and $d$ in the $n^{th}$ term formula, we get,

$73=3+(n-1)5$

$\Rightarrow n-1=\frac{73-3}{5}$

$\Rightarrow n-1=\frac{70}{5}$

$\Rightarrow n-1=14$

$\Rightarrow n=14+1$

$\Rightarrow n=15$

Hence, the value of $‘n’$ is $15$.