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Finding where a quadratic sequence passes 100

Patterns & sequences

Testing values in a quadratic sequence to find exactly where its terms first pass 100.

Challenge level
Exam standard
01
Have a go first

The Question

The nth term of a sequence is n² + 3n. Find the first term in the sequence that is greater than 100.

02
Then check together

The Answer

Reveal the Answer
108 (the 9th term)

Test values: n = 8 gives 88, n = 9 gives 108. Show the trial-and-improve reasoning rather than solving the inequality formally — it is faster and it is what the mark scheme accepts.

Now watch the solution

Finding where a quadratic sequence passes 100
Singapore Maths Academy
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Pencil and paper

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