Geometric Sequences

Question 1

A wrestling tournament begins with 128 competitors. In the first round, each competitor has 1 match against another wrestler. The winner of each match moves on to the next round until there is a winner. Write a sequence in which the terms represent the number of players still in the tournament at the end of each round. Describe the sequence? How many rounds are in the tournament?

Revolt · Accepted Answer

The sequence representing this situation is 64, 32, 16, 8, 4, 2, 1. The common ratio is 0.5 because only half of the wrestlers remain after each round. There are 7 rounds of matches until there is a single winner.

Question 2

The first four terms of a geometric sequence are 108, 36, 12, 4, …What is the common ratio?

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3111-14-03-20-03-task/mc001-1.jpg

Question 3

The 700th term in a geometric sequence is 20. If the common ratio of the sequence is 0.25, what is the 699th term?

Revolt · Accepted Answer

80

Question 4

Given the geometric sequence:–880, –220, –55, …The next term in the sequence is

Revolt · Accepted Answer

-13.75

Question 5

A sequence is defined by the following:What is the 4th term?

Revolt · Accepted Answer

–10.368

Question 6

A sequence is defined by the following: an = 4n – 1What is a1?0134

Revolt · Accepted Answer

1

Question 7

Question 8

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3111-14-03-20-07-task/mc001-1.jpg

Question 8

Question 9

Revolt · Accepted Answer

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Question 9

The fish population in a lake decreases by 2% each year.What is the common ratio?

Revolt · Accepted Answer

0.98

Question 10

What is a8?4847✔ 16,38465,536

Revolt · Accepted Answer

✔ 16,384

Geometric Sequences Answers

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