Question

A student goes to play baseball 6 miles away from his home riding a bicycle. In $1^{st}$ mile 100 calories are spent. In $2^{nd}$ mile 300 calories are spent. For further miles, number of calories are spent in the arithmetic sequence.
What is the range of relation from set of distance covered to set of number of calories spent?

• A. $\{100,300,500,700,900,1100\}$
• B. $\{100,300,400,500,900,1100\}$
• C. $\{100,300,500,700\}$

Answer 1

The correct option is A $\{100,300,500,700,900,1100\}$

A student travel $6$ miles to play baseball by riding bicycle.
Given that calories spent in every mile is in arithmetic sequence.
For $1^{st}$ mile calorie spent are $100$
For $2^{nd}$ mile calorie spent are $300$
For subsequent distance $200$ calories are added to the preceding calories spent.
So, calories spent for furthur miles will be,
$300+200=500$ calories for $3^{rd}$ mile.
$500+200=700$ calories for $4^{th}$ mile.
$700+200=900$ calories for $5^{th}$ mile.
$900+200=1100$ calories for $6^{th}$ mile.

The relation from set of distance covered (in miles) to set of number of calories spent is
$R:\left\{\right(1,100),(2,300),(3,500),(4,700),(5,900),(6,1100\left)\right\}$

So, Range of the relation is
$\{100,300,500,700,900,1100\}$.