Copy and continue the numerical sequences: a) 3, 6, 9, 12, _____, _____, _____ b) 27, 23, 19, 15, 11, _____, _____, _____ c) 1, 4, 9, 16, 25, _____, _____, _____ d) 2, 3, 5, 7, 11, 13, _____, _____ SOLUTION: a) 3, 6, 9, 12, 15, 18, 21 multiples of three b) 27, 23, 19, 15, 11, 7, 3, -1 subtract 4 from the previous term c) 1, 4, 9, 16, 25, 36, 49, 64 perfect squares d) 2, 3, 5, 7, 11, 13, 17, 19, 23 prime numbers SOLVE A SIMPLER PROBLEM EXAMPLE 6 The houses on Main Street are numbered consecutively from 1 to 150. How many house numbers contain at least one digit 7? SOLUTION: 1st. Understand the problem. Examples: 7, 73, 27, 117 2nd. Devise a plan. Separate this into simpler problems. 3rd. out the plan. First consider: How many house numbers contain the digit 7 in the unit’s place? Answer: This occurs once in every set of 10 consecutive numbers. For houses numbered 1 to 150, there are 15 distinct sets of 10 consecutive numbers, so 15 house numbers contain the digit 7 in the unit’s place. Second consider: How many house numbers contain the digit 7 in the ten’s place? Answer: There are ten: 70 through 79. However we already counted the number 77 already so we can’t count that twice. Final answer: 24 house numbers contain at least one digit 7. 4th. Look back. Are there other ways to do this? What if the house numbers are numbered up to 1000? it be much more work to count the ones that have at least one digit 7? Practice 12. The houses on Market Street are numbered consecutively from 1 to 150. How many house numbers contain at least one digit 4? SOLUTION:
Copy and continue the numerical sequences: a) 3, 6, 9, 12, _____, _____, _____ b) 27, 23, 19, 15, 11, _____, _____, _____ c) 1, 4, 9, 16, 25, _____, _____, _____ d) 2, 3, 5, 7, 11, 13, _____, _____ SOLUTION: a) 3, 6, 9, 12, 15, 18, 21 multiples of three b) 27, 23, 19, 15, 11, 7, 3, -1 subtract 4 from the previous term c) 1, 4, 9, 16, 25, 36, 49, 64 perfect squares d) 2, 3, 5, 7, 11, 13, 17, 19, 23 prime numbers SOLVE A SIMPLER PROBLEM EXAMPLE 6 The houses on Main Street are numbered consecutively from 1 to 150. How many house numbers contain at least one digit 7? SOLUTION: 1st. Understand the problem. Examples: 7, 73, 27, 117 2nd. Devise a plan. Separate this into simpler problems. 3rd. out the plan. First consider: How many house numbers contain the digit 7 in the unit’s place? Answer: This occurs once in every set of 10 consecutive numbers. For houses numbered 1 to 150, there are 15 distinct sets of 10 consecutive numbers, so 15 house numbers contain the digit 7 in the unit’s place. Second consider: How many house numbers contain the digit 7 in the ten’s place? Answer: There are ten: 70 through 79. However we already counted the number 77 already so we can’t count that twice. Final answer: 24 house numbers contain at least one digit 7. 4th. Look back. Are there other ways to do this? What if the house numbers are numbered up to 1000? it be much more work to count the ones that have at least one digit 7? Practice 12. The houses on Market Street are numbered consecutively from 1 to 150. How many house numbers contain at least one digit 4? SOLUTION:
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