Arithmetic Sequence

Question

Matrioshka dolls are Russian nesting dolls where bigger doll houses a smaller doll, and so on, as suggested in the picture. Suppose the doll’s weight progresses in a geometric pattern. If the largest doll weights 0.5kg and each smaller is 60% of the weight, what is the total weight of a set of Matrioshka dolls that contain 7 dolls?

Answer 1

To answer this question we can set up a table.  We will call the largest doll Doll #1, and the smallest doll Doll #7.

kg

Doll #                    Weight                    

1                             0.5kg

2                             60% of 0.5kg = 0.3kg (to find the weight multiply 0.5 by 0.6 (0.6 equals 60%) to get 0.3kg)  

3                             60% of 0.3kg = 0.18kg ( multiply 0.3 (the weight from Doll #2) by 0.6 (60%) to get 0.18kg)

4                             60% of 0.18kg = 0.108kg (multiply 0.18 (weight of Doll #3) by 0.6 (60%) to get 0.108kg)

5                             60% of 0.108kg= 0.0648kg (multiply Doll #4 by 0.6)

6                             60% of 0.0648kg= .03888kg (multiply Doll #5 by 0.6)

7                             60% of 0.3888kg = 0.023328kg (Multiply Doll #6 by 0.6)

 

Then add all of the weights together to get the total weight: 

0.5+0.3+0.18+0.108+0.0648+0.3888+0.02332 =  1.56492kg