Geometric Series Assignment
The formula is much faster
A
Which summation represents the total number of pennies on the chessboard?
A
The sequence formed is geometric, with a1 and common ratio r =
1 2
The total number of pennies on Row 1 is: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 =
255
How many pennies are on square 64
2^ 63
How many squares are on the chessboard?
64
How many pennies are on the chessboard?
B
How many pennies are on the nth square?
B
Which formula can be used to sum the first n terms of a geometric sequence?
B
Square 33 is the first square in Row 5, the first square of the second half of the chessboard. How many pennies are on square 33?
B 2^32
How many pennies would be on the square labeled H?
C 2^7
The number of pennies on square 33 is the sum of ALL the pennies on the first half of the chess board.
Greater than
The number of pennies on square 64 is the total number of pennies on the first 63 squares.
Greater than
Explain how you should use the formula to calculate the number of pennies on Rows 1-4. Why use the formula?
The formula is much faster
How many pennies are on each square?
a= 1 b= 2 c= 4 d= 8 e= 16 f= 32 g= 64 h= 128
compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?
my estimate was wrong i just added plus 2 when i was doubling the whole previous number.
