# Arithmetic Series

In a race, 8 apples are placed 5 meters apart on straight line, the first being 5 meters away from a basket. A contestant starts from the basket and puts one apple at a time into the basket. Find the total distance a contestant must run to finish the race.

-
We seem to be assuming that the basket is on the extension of the line segment containing the apples, although this is nowhere stated in the problem. – Gerry Myerson Feb 4 '13 at 9:07

You can undoubtedly find the answer. Draw a picture. Basket. Eight apples. They can be dots.

The nearest apple involves running a total of $10$ metres, The next, $20$. The next, $30$, And so on. Add up.

Remark: The numbers $10$, $20$, $30$, and so on form an arithmetic progression, or arithmetic series. There is a nice formula for the sum of such a thing. Probably it has already been done in your book, if not you can look it up. After you do, calculate the total in two ways, using the formula and directly by adding up.

-

Distance covered for 1st apple = 5+5=10

Distance covered for 2nd apple = 10+10=20

Distance covered for 3rd apple = 15+15=30

Distance covered for 4th apple = 20+20=40

Distance covered for 5th apple = 25+25=50

Distance covered for 6th apple = 30+30=60

Distance covered for 7th apple = 35+35=70

Distance covered for 8th apple = 40+40=80

Thus Total distance = 10+20+30+40+50+60+70+80

Sum of Arithmetic progression can be given using any one of following formula :

Putting the above values in formula : n=8 , $a_1=10$ , $a_n=80$

Thus we get , ANSWER as 360.

-