Problem 5 · 2018 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequence
The sum of 5 consecutive whole numbers is \(10^{2018}\). What is the middle number of those numbers?
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Answer: E — \(2\cdot 10^{2017}\)
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Hint 1 of 2
For five consecutive numbers, the sum is just five times the middle one.
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Hint 2 of 2
Divide the total by 5 to get the middle number.
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Approach: the sum of 5 consecutive numbers is 5 times the middle one
- Five consecutive whole numbers add up to 5 times the middle number.
- So the middle number is \(10^{2018}\div 5 = \frac{10^{2018}}{5}\).
- Since \(\frac{10}{5}=2\), this equals \(2\cdot 10^{2017}\).
- The middle number is \(2\cdot 10^{2017}\).
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