Sigma Notation and the nth Term

Meagan W.

ICM Honors

    The fairies in The Enchanted Garden are trying to figure out how many flowers are in The Enchanted Garden. There are many rows of flowers in the garden. In the first row there are 78 flowers. In every row 18 more flowers are added. What are the number of flowers in the nth row? If there are 62 rows of flowers how many flowers are in the 62nd row? How many flowers are in the entire Enchanted Garden if there are 180 rows of flowers? Put the 180th row in sigma notation.

• Use the formula a_n= a+(n-1)d  to find the the number of flowers in the 62nd row.

•  a_n= 78+ (62-1)18

• a_n= 78+ (61)18

• a_n= 78+1098

• a_n= 1176

• There are 1176 flowers in the 62nd row.

• Use a_n= a+ (n-1)d to find the nth number of flowers in The Enchanted Garden.

• a_n= 78+ (n-1)18

• a_n= 78+18n+18

• a_n= 96+18n

• The nth number of flowers in The Enchanted Garden is 6(3n+16).

• Use an= a+ (n-1)d to find the amount of flowers in the whole entire Enchanted Garden.

• an= 78+ (180-1)18

• an= 78+(179)18

• an= 78+3222

• an=3300

• There are 3300 flowers in the Enchanted Garden.

•  Draw a sigma sign. Above the sigma sign is placed a 180 since there are 180 rows. Below the sigma sign is placed n=1 because the sequence begins with 1 as n. Inside the sigma sign is the equation for the nth term which is (18n+96) o r 6(3n+6). 

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Links

Website that supports Sigma Notation and the nth term:

http://www.alltel.net/~okrebs/page136.html

Website that supports the nth Term:

http://www.maths-help.co.uk/Knowldge/Num/Nth_term/Question.htm

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