Problem 4 · 2009 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequenceoff-by-one
Harry does his paper round in Long Street. He has to deliver one newspaper to each house with an odd number. The first house with an odd number is 15 and the last house is number 53. How many houses does Harry have to visit?
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Answer: B — 20
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Hint 1 of 2
List the odd house numbers: 15, 17, 19, …, 53.
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Hint 2 of 2
Count terms in an arithmetic list with: (last − first)/step + 1.
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Approach: count terms of an arithmetic progression
- The houses are 15, 17, 19, …, 53, stepping by 2.
- Number of terms = (53 − 15)/2 + 1 = 38/2 + 1 = 19 + 1 = 20.
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