Findings about the influence of format on the range of strategies were inconclusive but analysis indicated sporadic evidence of possible influences. Work out the first differences between the terms. Building from Square and Factor Search were the most successful methods of Building a Relationship. Example two Work out the (n)th term of the sequence 5, 11, 21, 35. In this sequence, there is a second common difference of 4. Sequence of Differences was the most common strategy, but Building a Relationship was more likely to lead to the right formula. At least four numbers are needed to determine whether the sequence is quadratic or not. Qualitative analysis of eye-tracking data offers several strategies: Sequence of Differences, Building a Relationship, Known Formula, Linear Recursive and Initial Conjecture. Our aims are to identify their strategies and to explore whether and how format influences these strategies. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. This formula will have the form sn an2 + bn + c where the subscript n is the index of the term sn sn is the nth term in the sequence a, b, and c are constant values (where a is not zero). In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. After we determine that we have a quadratic sequence, we can find the general term for the sequence (the quadratic sequence formula).
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