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

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Using the properties and formula of Aritmetica series and Geometri series

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

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

Problem 1 :..... 8 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

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

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

U 2 =2U 1 2 = 2U 1 U 1 = 2/2 U 1 = 1 So the series : 1+2+4+.... a=1 r = U 2 /U 1 = 2/1 = 2

U n =ar n = 1x2 5 = 32

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

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 = 200-240 = -40

U n =a+(n-1)d U 4 =240+(4-1)-40 =240+(3)-40 =240-120 =120 U 5 =240 +(5-1)-40 =240+(4)-40 =240-160 =80

S n =1/2.n(2a+(n-1)d) S 4 =1/2.4(2x240+(4-1)-40) =2(480+3(-40)) =2(480-120) = 2x360 = 720

or S n =1/2.n(a+U n ) S 4 =1/2.4(240+120) = 2(360) = 720

S 5 =1/2.(5)(2(240)+(5-1)(-40)) =5/2.(480+4(-40)) =5/2.(480-160) =5/2.(320) =800

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

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