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
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B
3,250
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C
3,660
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D
3,560
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Solution
The correct option is B3,250 The sequence is 100,150..... a=100,d=50 First find the common difference: an=a1+(n−1)d a10=100+(10−1)50 =100+9×50 a10=550 We know that, Sn=n2 [First term + Last term] =102[100+550] =5[650] S10=3,250 So, the total number of students in 10 departments is 3,250.