Inductive Reasoning Practice

For each pattern below give the next three terms.

17, 23, 29, 35, 41,​ (a)   ,​ (b)   ,​ (c)  

• 47
• 53
• 59
• 48
• 46
• 52
• 58
• 57

For each pattern below give the next three terms.

-4, 8, -16, 32,​ (a)   ,​ (b)   , ​ (c)  

• -64
• 128
• -256
• 64
• -128
• 256
• -72
• 72
• 40
• -40

For each pattern below give the next three terms and explain how you know this.

100, 81, 64, 49, _______, ________, ________

• The next three terms are 36, 25, and 16. This is because the pattern consists of perfect squares: 10^2 (100), 9^2 (81), 8^2 (64), 7^2 (49), 6^2 (36), 5^2 (25), and 4^2 (16).

• The next three terms are 48, 36, and 24. This is because the pattern decreases by 12 each time.

• The next three terms are 40, 30, and 20. This is because the pattern decreases by 10 each time.

• The next three terms are 45, 35, and 25. This is because the pattern decreases by 15 each time.

For each pattern below give the next three terms and explain how you know this.

2, 10, 7, 15, 12, 20 ________, ________, ________

• The next three terms in the pattern are 17, 24, and 21. This is determined by observing the alternating addition and subtraction of numbers in the sequence.

• The next three terms in the pattern are 18, 25, and 22. This is determined by observing the alternating addition and subtraction of numbers in the sequence.

• The next three terms in the pattern are 16, 23, and 20. This is determined by observing the alternating addition and subtraction of numbers in the sequence.

• The next three terms in the pattern are 19, 26, and 23. This is determined by observing the alternating addition and subtraction of numbers in the sequence.

For each pattern below give the next three terms and explain how you know this.

7, 1, 4, -2, 1, -5, _______, ________, _______

• The next three terms in the pattern are -11, -17, -23. This is determined by observing the differences between consecutive terms: -6, 3, -6, 3, -6, which indicates a repeating pattern of subtracting 6 and adding 3.

• The next three terms in the pattern are -7, -9, -11. This is determined by observing the differences between consecutive terms: -2, -2, -2, which indicates a pattern of subtracting 2.

• The next three terms in the pattern are 0, -3, -6. This is determined by observing the differences between consecutive terms: -5, -3, -3, which indicates a pattern of subtracting 3.

• The next three terms in the pattern are -8, -14, -20. This is determined by observing the differences between consecutive terms: -6, -6, -6, which indicates a pattern of subtracting 6.

For each pattern below give the next three terms and explain how you know this. (Shapes) , ______, ______, ______

For each pattern below give the next three terms and explain how you know this. 7. (Dots) , ______, ______, ______

For each pattern below give the next three terms and explain how you know this. 8. (Arrows) , ______, ______, ______

• The next three terms in the pattern are determined by analyzing the given sequence of arrows and identifying the rule that governs the pattern.

• The next three terms are random and do not follow any specific rule.

• The pattern is based on colors, not shapes, so the next terms are colored arrows.

• The sequence is alphabetical, so the next terms are letters.

Recall: A conjecture is a statement believed to be true based on ________________ __________________.

• facts

• option

• inductive reasoning

• deductive reasoning

Are the following conjectures always true? If not, give a counterexample. 1. If a number ends in 7, it's a prime number.

• Yes, it is always true.

• No, it is not always true. For example, 27 is not a prime number.

• No, it is not always true. For example, 37 is not a prime number.

• No, it is not always true. For example, 47 is not a prime number.