Question

There are $100$ students in science department, $150$ students in computer science department in a higher secondary school and so on in an arithmetic sequence. What is the total number of students in $10$ departments?

• A. $3,960$
• B. $3,250$
• C. $3,660$
• D. $3,560$

Answer 1

The correct option is B $3,250$

The sequence is $100,150.....$
$a=100,d=50$
First find the common difference:
$a_n=a_1+(n-1)d$
$a_{10}=100+(10-1)50$
$=100+9\times 50$
$a_{10}=550$
We know that, $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{10}{2}[100+550]$
$=5\left[650\right]$
$S_{10}=3,250$
So, the total number of students in $10$ departments is $3,250$.