294

Quadratic Sequences Question 1.

Find an expression, in terms of \(n\), for the \(n\)th term of the sequence that has the following first five terms:

$$6 \qquad 13 \qquad 23 \qquad 36 \qquad 52 $$

131

Quadratic Sequences Question 2.

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

Pattern

(a) Find an expression, in terms of \(n\), for the number of red tiles in pattern \(n\).

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 expression, in terms of \(n\), for the total number tiles in Pattern \(n\) giving your answer in its simplest form.

(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.

170

Quadratic Sequences Question 3.

Here is a picture of four models. Some of the cubes are hidden behind other cubes.

cube models

Model one consists of one cube. Model two consists of four cubes and so on.

(a) How many cubes are in the third model?

(b) How many cubes are in the fourth model?

(c) If a fifth model were built, how many cubes would it take?

(d) Find an expression for the number of cubes used in the nth model.

(e) Sketch a side view, front view and plan view of the fourth model.

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