Math CentralQuandaries & Queries


Question from Emily, a student:

I don't understand how to do this question:
Nth term for 9, 7, 5, 3, 1
Is there a fast way to do nth term for this question? Or in fact any question?

Hi Emily,

There is no general fact or easy way to find the general term of a sequence. In fact for some sequences it can be very difficult. If you go to our Quandaries and Queries page and use the Quick Search to search for nth term you will see a variety of questions of this type we have received and how we have approached them.

Looking at your sequence $9, 7, 5, 3, 1$ I see that each term is $2$ less than the previous term so you could write it as

\[9, 9 - 2, 9 - 2 \times 2, 9 - 3 \times 2, 9 - 4 \times 2.\]

Hence you can write the $n^{th}$ term as $9 - (n-1) \times 2$ where $n$ starts at 1. You might want to simplify this expression.


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