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.
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