Question

One walker was sponsored
$100 plus $5 for the first kilometre, $10
for the second kilometre, $15 for the
third kilometre, and so on. How far
would this walker need to
walk to earn $150?

(I know it is 4 km, but I can't figure out how to write the general term.)

Answer 1

You have his earnings as

100+5+10+15+...
Since he gets $100 just for entering, all he needs to do is walk enough miles to get another $50

5+10+15+... is an arithmetic series of n terms, where

Sn = n/2 (2*5+(n-1)5) >= 50
n >= 4

Check: 5+10+15+20 = 50

Answer 2

Thank you!