A train can travel $200\ m$ in the first hour, $400\ m$ the next hour, $600\ m$ the third hour and so on in an arithmetic sequence. What is the total distance the train travels in $5$ hours?

Given: A train can travel $200\ m$ in the first hour, $400\ m$ the next hour, $600\ m$ the third hour and so on in an arithmetic sequence.

To do: To find the total distance the train travels in $5$ hours.

Solution:

The sequence is $200,\ 400,\ 600.....$

$a=200,\ d=200$

First find the common difference:$a_n=a+( n-1)d$

$a_5=200+( 5-1)200$

$=200+4\times200$

$a_5=1,000$

We know that, $S_n=\frac{n}{2}[First\ term + Last\ term]$

$=\frac{5}{2}[200+1,000]$

$=2.5[1,200]$

$\Rightarrow S_5=3,000$

Hence, the train will travel $3,000\ m$ in $5$ hours.
 

Updated on: 10-Oct-2022

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