Introduction to College Math: Sequences and Series: Sigma Notation and the nth Term
by: Winnie L

The sigma notation, S, is the universal symbol for arithmetic summation.     

  Plug in n into the equation, 3n+2,   until n reaches 7, the number on top.

3(1)+2=5  3(2)+2=8  3(3)+2=11  3(4)+2=14  3(5)+2=17  3(6)+2=20  3(7)+2=23

Now, find the total sum.                                           

5+8+11+14+17+20+23=98

Brian is responsible for purchasing seats for the Hurricanes game at the RBC center. In the first row, there are 200  seats. In each additional row,  20 seats are added. How many seats will be there in the nth row? How many seats are there in the RBC center if it has 40 rows?

To find how many seats there will be in the nth row, we can use the following formula: a_n=a + (n-1)d                 a: the first term(200 seats) d: distance between(20 seats)

=200 + (n-1)20

=200 +20n-20

=180+20n      There are 180+20n in the nth row.

To find how many seats there are overall, use the following formula:

a_n=a + (n-1)d        a=200   n=40rows d=20                 

=200+(40-1)20

=980 seats in the 40th row

S_n=n/2 (a+a_n)             n: number of terms(40) a: the first term(200 seats)  a_n:980 seats

=40/2(200+980)

=23600       There are 23,600 seats in the RBC center.                     

  The series above can also be written as .

[180+20(1)]=200 + [180+20(2)]=220 + [180+20(3)]=240 +. . .+[180+20(40)]=980

Sum: 200+ 220+ 240+ . . .+980=23,600 seats

Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.

Chinese Proverb

This quote reflects kindness. It means that teaching someone can benefit their entire life rather than giving something that is only temporarily beneficial.
http://tqpage.com/

An additional website about the summation notation: http://education.tjc.edu/math/Comp_004/comp_004.4.htm

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