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There are 100 students in science department, 150 students in

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?

3, 960

3, 250

3, 660

3, 560

Views: 640 students

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Emma Discussed

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?

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

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 [650]

S_{10} = 3, 250

So, the total number of students in

10

departments is

3, 250

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Question Text	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?
Answer Type	Text solution:1
Upvotes	150