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 $15^{t h}$ day?

7, 960

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7, 250

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7, 660

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7, 350

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Solution

The correct option is D $7, 350$
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 $15^{t h}$ day is $7, 350$ .

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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 15th day?

The correct option is D 7,350The sequence is 210,250,290..........a=210,d=40First find the common difference:an=a1+(n−1)da15=210+(15−1)40=210+14×40a15=770We know that, Sn=n2 [First term + Last term]=152[210+770]=7.5[980]S15=7,350So, the total number of visitors on 15th day is 7,350.

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 $15^{t h}$ day?