In a national treasure library, there are 10 visitors on first day, 50 visitors on second day and 90 visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on 5th day?

460

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450

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440

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430

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Solution

The correct option is B 450
The sequence is 10, 50, 90 ......
$a = 10, d = 40$
First find the common difference:
$a_{n} = a_{1} + (n - 1) d$
$a_{5} = 10 + (5 - 1) 40$
$= 10 + 4 \times 40$
$a_{5} = 170$
We know that, $S_{n} = \frac{n}{2}$ [First term + Last term]
$= \frac{5}{2} [10 + 170]$
$= 2.5 [180]$
$S_{5} = 450$
So, the total number of visitors on 5th day is 450

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In a national treasure library, there are 10 visitors on first day, 50 visitors on second day and 90 visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on 5th day?

The correct option is B 450The sequence is 10, 50, 90 ......a=10,d=40First find the common difference:an=a1+(n−1)da5=10+(5−1)40=10+4×40a5=170We know that, Sn=n2 [First term + Last term]=52[10+170]=2.5[180]S5=450So, the total number of visitors on 5th day is 450