Answers INMT3 Integrated Math 3 Sem 1 26-27Solving Polynomial Equations using Technology

Geometric Series Answers

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How many squares are on the chessboard?

Answer:

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How many pennies are on the nth square?

Answer not available

How many pennies are on each square? A = B = C = D = E = F = G = H =

Answers:

Blank 1:1

Blank 2:2

Blank 3:4

Blank 4:8

Blank 5:16

Blank 6:32

Blank 7:64

Blank 8:128

The total number of pennies on Row 1 is: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 =

Answer:

255

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

Answer not available

How else can the sequence for Row 1 be written? Notice:Square A: 1 penny = 20 Square B: 2 pennies = 21 Square C: 4 pennies = 22How many pennies would be on the square labeled H?

Answer not available

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

Option

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

232 – 1

232

232 + 1

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

mc001-1.jpg

mc001-2.jpg

mc001-3.jpg

Which of the following did you include?

The formula is much faster.

Substitute in a1=1, r = 2, and n = 32 into the formula.

How many pennies are on the chessboard?

264

264 – 1

264 – 232

There are 8 rows and 8 columns, or 64 squares on a chessboard. Suppose you place 1 penny on Row 1 Column A, 2 pennies on Row 1 Column B, 4 pennies on Row 1 Column C, and so on … Estimate: How many pennies in Row 1? pennies Estimate: How many pennies in Rows 1-4? pennies Estimate: How many pennies on the entire chessboard? pennies

Answers:

Blank 1:255

Blank 2:4,294,967,295

Blank 3:18,446,744,073,709,551,615

Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?

Answer:

My initial prediction was lower than the actual count of pennies on Row 1. To improve my estimate, I would count a small group of pennies and use that to better gauge the total across the row. The result was surprising because the pennies were packed much more tightly than I had anticipated.

Which of the following did you include?

a statement that your prediction was less than or greater than the actual count

a statement about how you would change your estimation process

Question text not available

Answer not available

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.

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

Your prediction was off by less than or equal to 1,000,000 of the actual total.

Your prediction was off by greater than 1,000,000 of the actual total.

After seeing the result for Rows 1-4, you would change your prediction for the total.

After seeing the results for Rows 1-4, you would not change your prediction for the total.

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.

Which of the following did you include?

The number of pennies doubles each time, so the count grows exponentially.

The number of pennies on Rows 5-8 will be much greater than on Rows 1-4.

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?

2^31

2^32

2^33

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