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Sums of five consecutive odd numbers

Sums of five consecutive odd numbers

IP 1
7 marks

The smallest of five consecutive odd numbers is \(2n+1\), where \(n\) is a whole number.

  1. Show that the sum of the five numbers is \(10n+25\).[2]
  2. The sum of five consecutive odd numbers is \(235\). Form and solve an equation to find the five numbers.[2]
  3. Explain why the sum of five consecutive odd numbers can never be \(2030\).[2]
  4. Find the largest possible sum that is less than \(1000\).[1]

Solution:

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Answer:(a) \(10n+25\) (b) \(43,45,47,49,51\) (c) \(10n+25\) is always odd and \(2030\) is even (d) \(995\)

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