tmua 2023 Q17

tmua · Uk · paper1 1 marks Geometric Sequences and Series Fractal/Iterative Geometric Construction (Area, Length, or Perimeter Series)

A circle $C _ { n }$ is defined by
$$x ^ { 2 } + y ^ { 2 } = 2 n ( x + y )$$
where $n$ is a positive integer.
$C _ { 1 }$ and $C _ { 2 }$ are drawn and the area between them is shaded.
Next, $C _ { 3 }$ and $C _ { 4 }$ are drawn and the area between them is shaded.
This is shown in the diagram.
This process continues until 100 circles have been drawn.
What is the total shaded area?

..... 19

A circle $C _ { n }$ is defined by

$$x ^ { 2 } + y ^ { 2 } = 2 n ( x + y )$$

where $n$ is a positive integer.

$C _ { 1 }$ and $C _ { 2 }$ are drawn and the area between them is shaded.

Next, $C _ { 3 }$ and $C _ { 4 }$ are drawn and the area between them is shaded.

This is shown in the diagram.

This process continues until 100 circles have been drawn.

What is the total shaded area?

Paper Questions

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