The nth term of a sequence

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Question from Michael, a parent:

My son has this question as part of his key stage 3 maths homework-

The nth term of a different sequence is n - 2/n^2.

We've got to find the first three terms of the sequence.

I've tried to help my son with this and we can up with -1, 0, 0.1.

Have we done this correctly, if not how do we work out the answer

Michael,

If the n² divides the whole expression before, that is, (n - 2)/n²,
then the first three terms are indeed
(1 - 2)/1² = -1, (2 - 2)/2² = 0,
(3 - 2)/n² = 1/9 \simeq 0.111 $\simeq$ 0.1.

But as you have written it here, I would interpret it as
n - (2/n²), whose first three terms are
1 - (2/1²) = -1, 2 - (2/2²) = 1.5, 3 - (2/3²) $\simeq$ 2.777

Claude

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