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Practice

4.15.5 Practice

4.15.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Here are the first two terms of a geometric sequence: 2, 4. What is the 5th term in the sequence?
  1. What are the common ratios of each geometric sequence?

    1. 1, 1, 1, 1
    1. 256, 128, 64
    1. 18, 54, 162
    1. 0.8, 0.08, 0.008
    1. 0.008, 0.08, 0.8
  1. A person owes $1,000 on a credit card that charges an interest rate of 2% per month.

Complete this table showing the credit card balance each month if they do not make any payments. Enter each answer to the hundredths place.

Month Total Bill In Dollars
1 1,000
2 1,020
3 1,040.40
4 a.
5 b.
6 c.
7 d.
8 e.
Table 4.15.0
    1. Month 4
      Round to the hundredths place.
    1. Month 5
      Round to the hundredths place.
    1. Month 6
      Round to the hundredths place.
    1. Month 7
      Round to the hundredths place.
    1. Month 8
      Round to the hundredths place.
  1. A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle with an area of 256 square inches, here are the first four steps:

A pattern of 4 congruent equilateral triangles. Starting with the first triangle, remove smaller congruent triangles to create the triangle to its right.

Complete this table showing the number of shaded triangles in each step and the area of each triangle. Enter each answer as an integer.

Step Number Number Of Shaded Triangles Area Of One Shaded Triangle In Square Inches
0 1 256
1 3 a.
2 b. c.
3 d. e.
4 f. g.
Table 4.15.1
    1. In Step 1, what is the area of each shaded triangle in square inches?
    1. In Step 2, what is the number of shaded triangles?
    1. In Step 2, what is the area of each shaded triangle in square inches?
    1. In Step 3, what is the number of shaded triangles?
    1. In Step 3, what is the area of each shaded triangle in square inches?
    1. In Step 4, what is the number of shaded triangles?
    1. In Step 4, what is the area of each shaded triangle in square inches?
  1. For each geometric sequence with missing terms, find the common ratio that might help determine the missing terms.

    1. ___, 5, 25, ___, 625
    1. –1, ___, –36, 216, ___
    1. 10, 5, ___, ___, 0.625
    1. ___, ___, 36, –108, ___
    1. ___, 12, 18, 27, ___