# Exam-Style Questions on Sequences Exponential Models

## Problems on Sequences Exponential Models adapted from questions set in previous Mathematics exams.

### 1.

IGCSE Extended

The diagrams above show a growing fractal of triangles. The sides of the largest equilateral triangle in each diagram are of length 1 metre.

In the second diagram there are four triangles each with sides of length $$\frac{1}{2}$$ metre.

In the third diagram there are 16 triangles each with sides of length $$\frac{1}{4}$$ metre.

(a) Complete this table for more diagrams.

 Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6 Diagram $$n$$ Length of Side 1 $$\frac{1}{2}$$ $$\frac{1}{4}$$ Power of 2 20 2-1 2-2

(b) Complete this table for the number of the smallest triangles in diagrams 4, 5 and 6.

 Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6 Diagram $$n$$ Number of smallest triangles 1 4 16 Power of 2 20 22 24

(c) Calculate the number of the smallest triangles in the diagram where the smallest triangles have sides of length $$\frac{1}{256}$$ metre.

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