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In a zoo, there are 210 visitors on first day, 250 visitors on

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In a zoo, there are $210$ visitors on first day, $250$ visitors on second day and $290$ visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on $1 5^{t h}$ day?

7, 960

7, 250

7, 660

7, 350

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In a zoo, there are

210

visitors on first day,

250

visitors on second day and

290

visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on

1 5^{t h}

day?

5 mins ago

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5 mins ago

Text solutionVerified

The sequence is

210, 250, 290..........

a = 210, d = 40

First find the common difference:

a_{n} = a_{1} + (n - 1) d

a_{15} = 210 + (15 - 1) 40

= 210 + 14 \times 40

a_{15} = 770

We know that,

S_{n} = \frac{n}{2}

[First term

+

Last term]

= \frac{15}{2} [210 + 770]

= 7.5 [980]

S_{15} = 7, 350

So, the total number of visitors on

1 5^{t h}

day is

7, 350

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Question Text	In a zoo, there are $210$ visitors on first day, $250$ visitors on second day and $290$ visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on $1 5^{t h}$ day?
Answer Type	Text solution:1
Upvotes	150