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Consecutive or alternate natural numbers meeting a sum condition: form a quadratic

This type of question, asked 2 times: CDS 1 2019, CDS 1 2021. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2019

    88
    The sum of the squares of four consecutive natural numbers is 294. What is the sum of the numbers ?

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  2. Question 2

    CDS 1 2021

    43
    The sum of the reciprocals of two alternate natural numbers is 724\frac{7}{24}. What is the sum of the numbers?

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