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Using the properties and formula of Aritmetica series and Geometri series.

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Presentation on theme: "Using the properties and formula of Aritmetica series and Geometri series."— Presentation transcript:

1 Using the properties and formula of Aritmetica series and Geometri series

2 INDICATOR Using the properties and formula of Arithmetic series and geometric series

3 WHAT WILL YOU LEARN Using the propertis and formula of aritmetic series and Geometric series

4 Problem 1 : cm 2 3 n Based on the figures above, determine : 1 cm 1.The next two stack the figure above 2.The number pattern of the figures according each height respectively 3.The total height of the figures until to 25 th term

5 Exercise 1.In 5 weeks, Mengky has been training to face the marathon competition. Each week he has to run twice time father than the week before in the 3 th week he runs 4 km. Determine the total distance for Mengky in five weeks training. 2.To file the job vacancy, a company hold a selection in many steps.In the first step, there are 240 applicants who join. In the second step there are 200 applicants who join. In the 3 th step there are 160 applicants who join. Determine the total applicants that will join in the 4 th and the 5 th step of selection

6 Given that U 2 =2U 1 n = 5 U 3 = 4km Asked : S 5 ? Solution U 3 = 2U 2 4 = 2U 2 U 2 = 4/2 U 2 =2

7 U 2 =2U 1 2 = 2U 1 U 1 = 2/2 U 1 = 1 So the series : a=1 r = U 2 /U 1 = 2/1 = 2

8 U n =ar n = 1x2 5 = 32

9 Next S n =a(r n -1)/r-1 S 5 =1(2 5 -1)/2-1 = 1(32-1)/1 = 1(31)/1 = 31

10 2.Given that U 1 =240 U 2 =200 U 3 =160 Asked :S 4,S 5 ? Solution U 1 =a =240 Difference (d) d = U 2 -U 1 = = -40

11 U n =a+(n-1)d U 4 =240+(4-1)-40 =240+(3)-40 = =120 U 5 =240 +(5-1)-40 =240+(4)-40 = =80

12 S n =1/2.n(2a+(n-1)d) S 4 =1/2.4(2x240+(4-1)-40) =2(480+3(-40)) =2( ) = 2x360 = 720

13 or S n =1/2.n(a+U n ) S 4 =1/2.4( ) = 2(360) = 720

14 S 5 =1/2.(5)(2(240)+(5-1)(-40)) =5/2.(480+4(-40)) =5/2.( ) =5/2.(320) =800

15 or S 5 =1/2.(5)(240+80) = 5/2.(320) = 800


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