TMUA 2023 Paper 1 Q17 — Worked Solution

P1·Coordinate Geometry, Sequences & Series·6.5Official · 2023 · Q17

circle-areacompleting-the-squarearithmetic-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?

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