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

Question 1200503: 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 the rest will it cover 120 inches?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
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 the rest will it cover 120 inches?
~~~~~~~~~~~~~~~~~~~

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.

Solved.

--------------------

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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