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Formula for Sum of n Terms of an AP

There are 25 ...

Question

There are 25 tourist in the first travel, 50 tourist the second travel and 75 tourist the third travel in the museum and so on in an arithmetic sequence. Find the total number of tourist in 25 travels?

A

8,460

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B

8,450

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C

8250

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D

8,125

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Solution

The correct option is C 8,125
The sequence is 25, 50, 75
$a = 25, d = 25$
First find the common difference:
$a_{n} = a_{1} + (n - 1) d$
$a_{25} = 25 + (25 - 1) 25$
$= 25 + 24 \times 25$
$a_{25} = 625$
We know that, $S_{n} = \frac{n}{2}$ [First term + Last term]
$= \frac{25}{2} [25 + 625]$
$= 12.5 [650]$
$S_{25} = 8, 125$
So, the total number of tourist in 25 travels is 8,125

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