SOLUTION: A ball starting from rest rolls down an inclined plane and passes over 3 in. during the 1st second, 5 in. during the 2nd second, 7 in. during the 3rd second, etc. In what time from

You have this arithmetic progression

    3, 5, 7, . . . 

and they want you determine how many terms are needed to get the sum of 120.


Let's consider the sum of the first n positive odd integer numbers

    1 + 3 + 5 + 7 + . . . + (2n-1).

adding the term "1" as a very first term.


It is well known fact that this sum is  .

So, we should find n in a way that 

    1 + 3 + 5 + 7 + . . . (2n-1) =  = 120 + 1 = 121.


For it, the value of "n" should be  n =  = 11.


So, the arithmetic progression 3, 5, 7, . . . should have 11-1 = 10 terms 
to have the sum equal to 120.


ANSWER. In 10 minutes.