Geometric Sequences Assignment

A sequence is defined by the following: an = 4n - 1 What is a1? What is a8?

B C

Select the sequences that are geometric. 18, 36, 54, 72, ... 4.1, 8.2, 16.4, 32.8, ... -7, 14, -28, 56, ... 980, 784, 627.2, 501.76, ... 5, 2, -1, -4, ... Which statements describe characteristics of a geometric sequence? Check all that apply. There is a common difference between terms Each term is multiplied by the same number to arrive at the next term. The sequence increases or decreases in a linear pattern There is a common ratio between terms.

2 3 4 2 4

Given the geometric sequence: -880, -220, -55, ... The next term in the sequence is ⇒ -13.75 The 700th term in a geometric sequence is 20. If the common ratio of the sequence is 0.25, what is the 699th term? 5 10 80

-13.75 c

Which formula can be used to find the nth term of the following geometric sequence? − 2 9 , 2 3 , −2, 6,...

A

A sequence is defined by the following: mc001-1.jpg What is the 4th term? -12.4416

B

The first four terms of a geometric sequence are 108, 36, 12, 4, ... What is the common ratio? -72 -3 3 mc001-1.jpg The fish population in a lake decreases by 2% each year. What is the common ratio?

D D

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your 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.

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.

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?

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.