Question

A company employed $400$ persons in the year $2001$ and each year increased by $35$ persons. In which year the number of employees in the company will be $785$?

Answer 1

We know that the formula for the nth term is $t_n=a+(n-1)d$, where $a$ is the first term, $d$ is the common difference.

It is given that a company employed $400$ persons in the year $2001$ and each year increased by $35$ persons, therefore, the first term $a_1=400$ and the common difference is $35$.

Also, the given $n$th term is $785$, therefore,

$t_n=a+(n-1)d\Rightarrow 785=400+(n-1)35\Rightarrow 785=400+35n-35\Rightarrow 785=365+35n\Rightarrow 35n=785-365\Rightarrow 35n=420\Rightarrow n=\frac{420}{35}=12$

Since, we find that there are $12$ terms in the A.P and also it is given that the last term is $t_{12}=785$.

Hence, in $2012$, the number of employees in the company will be $785$.