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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