Four concentric circles share the same centre. The smallest circle has a radius

Question

Four concentric circles share the same centre. The smallest circle has a radius of 1 inch. For n ≥ 1, the area of the nth smallest circle in square inches, A_n, is given by

A_{n + 1} = A_{n} + (2 n + 1) π

. What is the ratio of the sum of the areas of the four circles to the sum of their circumferences?

Answer: Option B
:
B
Following the pattern
A

_{1}

π

_{2}

π

_{3}

π

_{4}

=16

π

Hencer = 1,2,3 4
Thus
C

_{1}

= 2

π

_{2}

= 4

π

_{3}

= 6

π

_{4}

= 8

π

Ratio = 1.5

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