急! F6 Geometric Sequences 02q8

17. The sum of a geometric sequence to infinity exists when -1<1.
If a=2, the common ratio is 2a=4 which is greater than 1.

22.
(a)(i) area of AB1C1D1=2 cm^2
(ii), (iii) The rectangles are all similar and the areas of them are in geometric sequence with common ratio=(3/2)^2=9/4
The area of AB2C2D2=area of AB1C1D1 x (9/4)=9/2 cm^2
The area of AB3C3D3=area of AB2C2D2 x (9/4)=81/8 cm^2

(b) area of the figure
=area of AB6C6D6-area of AB5C5D5
=2x(9/4)^5-2x(9/4)^4=64.1 cm^2 (1 d.p.)<1.