Section 12.5
Sigma Notation and the nth Term
Jamie G.
Drew needs to bring a bucket of water to each of the crops of corn. The first row of has 15 crops of corn. Each additional row has an additional 5 crops of corn then the row before it. How many crops of corn will the 12th row have? How many crops of corn will be in the nth row? How many buckets of water will Drew need?
To find out the number of crops in the 12th row, use the arithmetic sequence.
an= a + (n-1)d
a15= 15 + (12-1)5
a15 = 15 + (11)5
a15 = 70 *There are 70 crops of corn in the 12th row*
To find out the number of crops in the nth row, use the same formula.
an = 15 + (n-1)(5)
an = 5n +10 *There are 5n +10 crops in the nth row*
To find the number of buckets Drew will need, use the sum of the arithmetic series formula.
Sn = (n/2)(a + an)
= (12/2)(15+70)
= 510 *Drew will need to have 510 buckets of water*
Sigma indicates a sum or series. 15 +17 +19...is a series. It can be written as follows :
To write this sigma notation in expanded form, just substitute the numbers 1-12 in for "n" as follows:
(5(1)+10) + (5(2)+10) + (5(3) + 10) + (5(4) + 10) ....
15 + 20 + 25 + 30 +....85 =510
For an infinite series:
Substitute 1, 2, 3, and 4 for n. Then use the formula Sn = a/(1-r)
Formula of n factorial: n!=n(n-1)(n-2) ...1
Example: 3!=3*2*1 = 6
Quote: "The best portion of a good man's life is his little, nameless, unremembered acts of kindness and of love." - William Wordsworth
What it means: The little things are what matter most in life.
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