Geometric Series Worksheet Solution4





In the page geometric series worksheet solution4 you are going to see solution of each questions from the geometric series worksheet.

(ii) 0.4 + 0.94 + 0.994 + ............

Solution:

   = 0.4 + 0.94 + 0.994 + ............

   =[ (1-0.6) +(1-0.6) + (1-0.06)  + ..............to  n terms]

   = (1+1+1+............to n terms) - (0.6+0.06+0.006+....... to n terms)

a = 1     r = 1/1

            r = 1

a = 0.6     r = 0.06/0.6

              r = 0.1  < 1

  Sn = na                           Sn = = a (1-r^n)/(1-r)

    =  n (1) - 0.6 [1-(0.1)^n]/(1-0.1)

    =  n (1) - 0.6 [1-(0.1)^n]/(0.9)

    =  n  - 0.6/0.9 [1-(0.1)^n]

    =  n  - 6/9 [1-(0.1)^n]

    =  n  - 2/3 [1-(0.1)^n]


(9) Suppose that five people are ill during the first week of an epidemic and each sick person spreads the contagious disease to four other people by the end of the second week and so on. By the end of 15th week,how many people will be affected by the epidemic?

Solution:

In the beginning of the problem five people are ill during the first week and each sick person spreads the contagious disease to four other people by the end of the second week. This is going to continue in the after weeks. Let us write this as sequence

             5, 5(4) , 5(4)² , ..............

             5, 20 , 80 , ..............

We need to make this sequence as series because we have to find total number of people affected by the epidemic.so the above sequence is going to become

             5 + 20 + 80 + ..............

here a = 5  r = 20/5         n = 15

                r = 4

        S n = a (r^n-1)/(r-1)

        S 15 = 5 (4^15-1)/(4-1)

        S 15 = (5/3) (4^15-1)


(10) A gardener wanted to reward a boy for his good deeds by giving some mangoes. He gave the boy two choices. He could either have 1000 mangoes at once or he could get 1 mango on the first day,2 on the second day,4 on the third day,8 mangoes on the fourth day and so on for ten days. Which option should the boy choose to get the maximum number of mangoes?

Solution:

We need to make this sequence as series because we need to find sum of mangoes in ten days. If the number of mangoes collected in this way is greater than 1000 we can say that this is the better way.

1 + 2 + 4 + 8 + ....... 10 days

Here a = 1       r = 2/1

                     r = 2 > 1

Sn = a (r^n-1)/(r-1)

    = 1 (2^10 - 1)/(2-1)  

    = 1 (2^10 - 1)/1  

    = 1024 - 1

    = 1023

In this way we get more mangoes than the previous way. So the boy has to choose the second way to get more mangoes.

These are the contents in the page geometric series worksheet solution4.



geometric series worksheet solution4