## Exam-Style Question on Sequences## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 131. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

The diagrams below show a sequence of patterns made from red and yellow tiles.

(a) Find an ex

The total number of red and yellow tiles in each pattern is always the sum of the squares of two consecutive whole numbers.

(b) Find an ex

(c) Is there a pattern for which the total number of tiles is 303? Give a reason for your answer.

(d) Explain why the total number of tiles in any pattern of this sequence is always an odd number.

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