Chapter 12.1 : Arithmetic Sequences and Series

by Tripp T

   There are a group of boys at Sanderson High School that truly enjoy Halo LAN parties.  For those of you who don't know what that is, Halo is a game for X-Box and a Halo LAN party is when two or more X-Boxes are hooked together through an ethernet cable and the boys play multiplayer Halo.  The game can become really addicting, as is evident by the amount of time these boys spend playing it.  It started at one hour on the first day, and then they started playing one half hour more every day after that. 

    One day a girl got smart with one of the boys and asked him how many hours they have Halo LAN parties in a given month.  Since the majority of them do well in I.C.M. class, they determined that the number of hours they have LAN parties in a month  could be found by finding the sum of the first 31 terms (31 days in a month) of the arithmetic series 1 + 1.5 + 2 + 2.5 +............. 

    First off, it is necessary to know the formulas that will be needed. 

To find the Nth term of a series, use the formula L = A + (n-1)d where n = the number of terms in the series, A = the first term in the series, and d = the common difference between the terms in the series.  

The formula with the variables will look like this:

                                                     L = 1 + (30).5          

 When the math is done, you will find that the 31st term in the series is 16, so on the 31st day, the boys will play 16 hours of Halo.  

Now that we know the first and final terms of the series we can use the formula S = .5N (A₁ + A_N) to find the sum of the series, giving us the total amount of hours the boys have Halo LAN parties in one month.  S represents the sum of the series, N still represents the number of terms in the series, A₁ is the first term, and A_N is the last term.      When the numbers are plugged in, the equation looks like this:    

                                                   S = .5(31) (1 + 16)

When the math is done on this formula, you will find that in one month, the boys spend   263.5 hours having Halo LAN parties.                                                         

BACK

-To put a lid on things, I'll finish with the following quote, which clearly shows an example of perseverance.  The band Dispatch said it best in their song "Elias".  "Distance is short when your hand carries what your eyes found."

-I think that means that if you can see what you want and stick to it, you can achieve the goal you saw in no time.                                                                                                               

                                                       This page was last updated:

                                                                03/14/03 01:00 PM