Question

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?

• A. $2,000$
• B. $3,000$
• C. $4,000$
• D. $5,000$

Answer 1

Answer: (B)

$3,000$

The sequence is $200,400,600.....$
$a=200,d=200$
First find the common difference:
$a_n=a_1+(n-1)d$
$a_5=200+(5-1)200$
$=200+4\times 200$
$a_5=1,000$
We know that, $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{5}{2}[200+1,000]$
$=2.5[1,200]$
$S_5=3,000$
Hence, the train will travel $3,000$ m in $5$ hours.