?Number Theory Jacqui made the following conjecture about the information in the table

Write a definition of conjecture.

Explain how you can show that a conjecture is false.

Write your own sequence of numbers. Then write a sentence that describes the pattern in the numbers.

Tell how to find the next term in each pattern. \(20,\ 26,\ 32,\ 38,\ \ldots\) Equation Transcription: Text Transcription: 20, 26, 32, 38, . . .

Tell how to find the next term in each pattern. \(10,\ 7,\ 4,\ 1,\ \ldots\) Equation Transcription: Text Transcription: 10, 7, 4, 1, . . .

Tell how to find the next term in each pattern. \(3,\ 6,\ 12,\ 24,\ \ldots\) Equation Transcription: Text Transcription: 3, 6, 12, 24, . . .

Tell how to find the next term in each pattern. \(30,\ 31,\ 33,\ 36,\ \ldots\) Equation Transcription: Text Transcription: 30, 31, 33, 36, . . .

Find the next three terms of each sequence. \(1,\ 3,\ 5,\ 7,\ \ldots\) Equation Transcription: Text Transcription: 1, 3, 5, 7, . . .

Find the next three terms of each sequence. \(9,\ 6,\ 3,\ 0,\ \ldots\) Equation Transcription: Text Transcription: 9, 6, 3, 0, . . .

Find the next three terms of each sequence. \(96,\ 48,\ 24,\ 12,\ \ldots\) Equation Transcription: Text Transcription: 96, 48, 24, 12,...

Find the next three terms of each sequence. \(7,\ 8,\ 11,\ 16,\ \ldots\) Equation Transcription: Text Transcription: 7, 8, 11, 16, . . .

Draw the next figure in the pattern.

Draw the next figure in the pattern.

Number Theory Jacqui made the following conjecture about the information in the table. If the first number is negative and the second number is positive, the sum is always negative. Find a counterexample for her conjecture.

Find the next three terms of each sequence. \(5,\ 9,\ 13,\ 17,\ \ldots\) Equation Transcription: Text Transcription: 5, 9, 13, 17, . . .

Find the next three terms of each sequence. \(12,\ 8,\ 4,\ 0,\ \ldots\) Equation Transcription: Text Transcription: 12, 8, 4, 0, . . .

Find the next three terms of each sequence. \(12,\ 21,\ 30,\ 39,\ \ldots\) Equation Transcription: Text Transcription: 12, 21, 30, 39, . . .

Find the next three terms of each sequence. \(1,\ 2,\ 4,\ 8,\ \ldots\) Equation Transcription: Text Transcription: 1, 2, 4, 8, . . .

Find the next three terms of each sequence. \(3,\ 15,\ 75,\ 375,\ \ldots\) Equation Transcription: Text Transcription: 3, 15, 75, 375, . . .

Find the next three terms of each sequence. \(2,\ -3,\ -8,\ -13,\ \ldots\) Equation Transcription: Text Transcription: 2,-3,-8,-13, . . .

Find the next three terms of each sequence. \(-1.4,\ 2.6,\ 6.6,\ 10.6,\ \ldots\) Equation Transcription: Text Transcription: -1.4, 2.6, 6.6, 10.6, . . .

Find the next three terms of each sequence. \(6,\ 7,\ 9,\ 12,\ \ldots\) Equation Transcription: Text Transcription: 6, 7, 9, 12, . . .

Find the next three terms of each sequence. \(13,\ 14,\ 16,\ 19,\ \ldots\) Equation Transcription: Text Transcription: 13, 14, 16, 19, . . .

Find the next three terms of each sequence. \(20,\ 22,\ 26,\ 32,\ \ldots\) Equation Transcription: Text Transcription: 20, 22, 26, 32, . . .

Find the next three terms of each sequence. \(10,\ 13,\ 19,\ 28,\ \ldots\) Equation Transcription: Text Transcription: 10, 13, 19, 28, . . .

Find the next three terms of each sequence. \(10,\ 17,\ 31,\ 52,\ \ldots\) Equation Transcription: Text Transcription: 10, 17, 31, 52, . . .

Draw the next figure in each pattern.

Draw the next figure in each pattern.

Draw the next figure in each pattern.

Draw the next figure in each pattern.

Draw the next figure in each pattern.

Draw the next figure in each pattern.

Find the next term in the sequence \(\frac{1}{2},\ \frac{3}{2},\ \frac{5}{2}\). Equation Transcription: Text Transcription: 1/2, 3/2, 5/2

What operation would you use to find the next term in the sequence \(3,\ 6,\ 12,\ 24,\ \ldots\)? Equation Transcription: Text Transcription: 3,6,12,24,...

Pets Find a counterexample for this statement: All dogs have spots.

Entertainment The graph shows the number of movie tickets sold yearly in the United States from 1993 to 2003. Predict the number of movie tickets that will be sold in 2006.

Law Enforcement All fingerprint patterns can be divided into three main groups: arches, loops, and whorls. Name a situation that would provide a counterexample to this statement.

Critical Thinking Find the total number of small triangles in the eighth figure of the pattern.

Multiple Choice Choose the expression that represents the value, in cents, of \(n\) nickels and \(d\) dimes. (Algebra Review) (a) \(n+d\) (b) \(10n+5d\) (c) \(5n+10d\) (d) \(15nd\) Equation Transcription: Text Transcription: n d n+d 10n+5d 5n+10d 15nd