Question

There are $200$ students in IT department, $210$ students in Computer science department and $220$ students in Mechanic department in the college, and so on in an arithmetic sequence. What is the total number of students in $8$ departments?

• A. $1,880$
• B. $1,760$
• C. $1,660$
• D. $1,560$

Answer 1

Answer: (A)

$1,880$

The sequence is $200,210,220.....$
$a=200,d=10$
First find the common difference:
$a_n=a_1+(n-1)d$
$a_8=200+(8-1)10$
$=200+7\times 10$
$a_8=270$
We know that, $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{8}{2}[200+270]$
$=4\left[470\right]$
$S_8=1,880$
So, the total number of students in $8$ departments is $1,880$.