The terms of a sequence are given by this equation where each term is found from the two preceding terms.

.For example if the first two terms are 2 and 5 then the next term is (1+5)/2=3 and the sequence is

2,  5,  3,  4/5,  3/5,  2,  5, … etc.

Investigate the sequences you get when you choose your own first two terms. What happens to your sequences?

Make a conjecture about the behaviour of sequences given by this rule.

Can you prove your conjecture?

This problem is adapted from the NRICH task Loopy with permission of the University of Cambridge. All rights reserved.

### 2 Responses to Grades 10 to 12 – Loopy

1. juliusmukama says:

The activities encourage critical thinking, I can’t miss to try them out in my Mathematics classes. Thanks Toni!

• toni says:

Please share your experience with other teachers telling them how the lesson worked out with your class, by writing another comment here (and also after other posts about different lesson activities).

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