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1. Today’s topic: Infinitely decreasing geometrical progression (IDGP)

2. ; By the end of the lesson students will be able to         Understand the formula of the Infinitely decreasing geometrical progression Solve problems by using the formula Convert periodical decimal to the simple fraction

3. Key terms Sequence Ariphmetical progression (AP) Geometrical progression (GP) Infinitely decreasing geometrical progression (IDGP) Common ratio Common difference

4. Let's recall ... What is the formula for the n th term of an arithmetic progression ? What is the formula of the n th term of the geometric progression ? What is the formula for the sum of the first n terms of an arithmetic progression ? What is the formula for the sum of the first n terms of a geometric progression?

5. Definition

6. Example 1 find the sum of IDGP .

7. Example 2

8. Берілген видеоматериалда шексіз геометриялық прогрессияның қосындысының анимация түріндегі шешімі көрсетілген

9. 0,33333 ... =0,(3) how to convert to the simple fraction? 0,3+0,03+0,003+… b1 = 0,1 q= 0,03 / 0,3 = 0,1 S= Example 3

10. Work with problems ...

11. (a) Find the sum to infinity of the GP with first term 3 and common ratio 1/2 (b) The sum to infinity of a GP is four times the first term. Find the common ratio. ( c) The sum to infinity of a GP is twice the sum of the first two terms. Find possible values of the common ratio. Answers 6 0,75 ± 1/ √ 2

12. Confirmation questions

13. 1. Find the formula of the IDGP

14. Given sequence 12,6, … Find the IDGP

15. Thanks for the attention!