AnswersDHS Algebra 2 VGeometric Series

Geometric Series Answers

17 verified answers
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The sequence formed is geometric, with a1 = , and common ratio r = .

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5

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10

Which formula can be used to sum the first n terms of a geometric sequence?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

Explain how you should use the formula to calculate the number of pennies on Rows 1-4. Why use the formula?

Answer:

The formula is much faster. Substitute in a1=1, r = 2, and n = 32 into the formula.

12

Which of the following did you include?

A
The formula is much faster.
B
Substitute in a1=1, r = 2, and n = 32 into the formula.
19

Which of the following is the total number of pennies on Rows 1-4 (the first 32 squares)?

A
232 – 1
B
232
C
232 + 1
20

Check every statement that is true about your prediction of the total pennies on Rows 1-4.

A
Your prediction was off by less than or equal to 1,000,000 of the actual total.
B
Your prediction was off by greater than 1,000,000 of the actual total.
C
After seeing the result for Rows 1-4, you would change your prediction for the total.
D
After seeing the results for Rows 1-4, you would not change your prediction for the total.
21

Explain why there are so many pennies on Rows 1-4. How do you think the number of pennies on Rows 5-8 will compare?

Answer:

The number of pennies doubles each row, causing exponential growth. Therefore, Rows 5–8 will contain much more than Rows 1–4.

22

Which of the following did you include?

A
The number of pennies doubles each time, so the count grows exponentially.
B
The number of pennies on Rows 5-8 will be much greater than on Rows 1-4.
29

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?

A
2^31
B
2^32
C
2^33
30

The number of pennies on square 33 is the sum of ALL the pennies on the first half of the chess board.

A
greater than
B
less than
C
equal to
33

The last square of the chessboard is square 64.How many pennies are on square 64?

A
2^61
B
2^62
C
2^63
34

The number of pennies on square 64 is the total number of pennies on the first 63 squares.

A
greater than
B
less than
C
equal to
37

Which summation represents the total number of pennies on the chessboard?

A
Option
Option A
B
Option
Option B
C
Option
Option C
38

How many pennies are on the chessboard?

A
264
B
264 – 1
C
264 – 232

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