Math CentralQuandaries & Queries


Question from claire, a student:

What is the explicit definition for the sequence 4,7,16,43,...?

We have two responses for you.

Hint: Think about powers of 3, Claire.

Stephen La Rocque.>


What you should realise is that there is no 'explicit definition' for your sequence. There are infinitely many sequences that start off 4, 7, 16, 43, ... . What you probably want is a quick way to find one such sequence that starts that way. One method is to look at the differences between consecutive terms in your sequence: 3, 9, 27. Does that suggest a pattern for the next difference and, if so, what is the next term in your sequence? Once you find that out then you can work out what the nth term looks like.


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