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Averages · Question 14 of 62

Question 14

MediumOriginal question

The average of the first n natural numbers is 18.5. What is n?

Options for question 14

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Average of 1 to n = n+12\frac{n+1}{2}.

  2. n+12=18.5⇒n+1=37⇒n=36\frac{n+1}{2} = 18.5 \Rightarrow n + 1 = 37 \Rightarrow n = 36.

Worth noting

37 is n+1n + 1. Treating the average as n/2n/2 also gives 37.

Concept
Working backwards from the average of the first n naturals
Typical time
45 s
Your time
—
The rule this testsSimple average
Practise this chapter →

Ten questions from Averages, at your own pace.

Practise this chapter →

Ten questions from Averages, at your own pace.