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Sequence and series- Project

Arithmetic sequence:

Geometric sequence:

An=a+(n-1)d

An=n/2(2a+(n-1)d)

Because the model an = 180.9(0.9)n º 5 gives the average monthly bill, the model

bn = 12(180.9)(0.9)n º 5 = 2170.8(0.9n) º 5 gives the average annual bill. Using

a1 = 2170.8 and r = 0.9, you can estimate a person’s total cost for cellular

telephone service during the 8 year period 1990–1997 to be:

Domestic bees make

their honeycomb by starting with a single

hexagonal cell, then forming ring after ring of

hexagonal cells around the initial cell, as

shown. The numbers of cells in successive

rings form an arithmetic sequence.

Source: USDA’s Carl Hayden Bee Research Lab

a. Write a rule for the number of cells in the nth ring.

b. What is the total number of cells in the honeycomb after the 9th ring

is formed? (Hint: Do not forget to count the initial cell.)

A7=7/2(2(2170)+(7-1).9)=15208.9

a1=6+(1-1)6=6

a1=6,a2=12,...a6=?,an=?

a2=6+(2-1)6=12

a6=6+(6-1)6=36

an=a1(n-1)d

monthly bills

honeycombs

by Victor Simpson

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