16.3 GeometricProgression 等比数列

1.
Each year, the price of an electric equipment increase by 5% of its price in the previous year. Given that the price of the electric instrument is RM800 at the beginning. State its price after n years, in terms of n. Hence, find the price after 10 years, to the nearest ringgit.

每年电子设备的价格会比前一年的价格增加5%。已知开始时电子仪器是RM800. 以n表示，n 年后的价钱。据此，求10年后的价钱，答案准确至令吉

Figure beside shows a triangle ABC with right angle at B, angle ACB = β and BC = a. Point D is the leg of the perpendicular line from B to AC, and the same way to define E and F.
如右图所示一三角形ABC 其中 B 为直角, 角 ACB = β 和 BC = a. 点 D 是从B 到 AC的垂足, 以此类推来定义 E 和 F.

(a) State angle ABD in terms of β.
以β表示角ABD.

(b) State BD and DE in terms of a and β.
以a 和 β表示BD 和DE。

(c) Show that the lengths of CB, BD, DE are in geometric progression.
证明CB, BD, DE的长度成等比。

3.
A circle with radius 10cm is divided into 4 sectors where the areas of the sectors are in geometric progression. Given that the area of the largest sector is 8 times of the area of the smallest sector, find the area of the largest sector.

一半径为10cm 的圆被分成4个扇形使得那些扇形的面积成等比数列。已知最大的扇形面积是最小的扇形面积的8倍，求最大的扇形面积。

4.
In an G.P. if the sum of the first six terms is nine time of the sum of first three terms, find the common ratio.

在一等比数列，若首六项的和是首三项的和的9倍，求公差。

5.
In 1960 a man earned RM2000 and spent it all. During the next 10 years his salary increased by 5% per annum (compound interest|), but inflation caused his expenditure to rise by 4% per annum (compound interest). Find how much he had saved by the end of 1970, giving your answer to two significant figures.

在1960年某人赚RM2000并花完了。接下来的10年他的薪水每年增加5%(复利计算), 但通货膨胀造成他每年的开销每年增加4%(复利计算). 请问到1970年尾他可以存多少钱，答案用两位有效数字表示。

6.
If a, b, c are in G. P., prove that in A. P.

若a, b, c 成等比数列, 试证 成等差数列。