### 第十七章：指数函数与对数函数 exponential function and logarithmic function

16.2 等差数列 Arithmetic Progression
16.2 Arithmetic Progression 等差数列
1.
Given that the 11 term of an arithmetic progression is 34, find the sum of the 3 term, 9 term and 21 term.

102
2.
Figure beside shows few circles where their radii increase by 1cm as follow on. Given that the total length of perimeter of the first five circles is 120 cm, find the length of radius for the smallest circle.

10 cm
3.
The n term of a arithmetic progression is represented as T and the sum of first n terms is represented as S. Given that T + T = 40 and S :S = 2 : 3.
T 表示一等差数列的第n项而 S 表示首n项的和。已知 T + T = 40 和 S :S = 2 : 3.

(a) Calculate the value of the first term and the common difference.

(b) Find the value of S.

(a) 5, 2

(b) 1020

4.
Figure beside shows three right angle triangle which has a fixed base and height decreasing 2 units as follow on.

(a) Show that the area of the three triangles is an arithmetic progression.

(b) If the areas of the following triangles have the same characteristic as above, given the total area of first six triangles is 1620cm, find the area of the first triangle.

(c) Calculate the total area of all triangles that was formed.

(b) 300

(c) 3900cm

5.
Find the sum of all integers divisible by 4 and 7, lying between 400 and 700.