2.1. Inductive Reasoning http://www.ck12.org
2.
- Use the pattern below to answer the questions.
a. Draw the next figure in the pattern.
b. How does the number of points in each star relate to the figure number?
c. Use partbto determine a formula for thenthfigure.- Use the pattern below to answer the questions. All the triangles are equilateral triangles.
a. Draw the next figure in the pattern. How many triangles does it have?
b. Determine how many triangles are in the 24thfigure.
c. How many triangles are in thenthfigure?For questions 5-12, determine: 1) the next two terms in the pattern, 2) the 35thfigure and 3) the formula for thenth
figure.
- 5, 8, 11, 14, 17,...
- 6, 1, -4, -9, -14,...
- 2, 4, 8, 16, 32,...
- 67, 56, 45, 34, 23,...
- 9, -4, 6, -8, 3,...
10.^12 ,^23 ,^34 ,^45 ,^56 ,...
11.^23 ,^47 , 116 , 158 ,^1019 ,... - 3, -5, 7, -9, 11,...
- -1, 5, -9, 13, -17,...
- − 21 ,^14 ,− 61 ,^18 ,− 101 ,...
- 5, 12, 7, 10, 9,...
- 1, 4, 9, 16, 25,...
For questions 13-16, determine the next two terms and describe the pattern.
- 3, 6, 11, 18, 27,...
- 3, 8, 15, 24, 35,...
- 1, 8, 27, 64, 125,...
- 1, 1, 2, 3, 5,...
We all use inductive reasoning in our daily lives. The process consists of making observations, recognizing a pattern
and making a generalization or conjecture. Read the following examples of reasoning in the real world and determine
if they are examples of Inductive reasoning. Do you think the conjectures are true or can you give a counterexample?