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Ana started off her penny collection with 1 penny. She then adds 5 pennies to her penny collection each day.

how could you change the above scenario to make it a geometric series rather than an arithmetic series?

 Using the answer, how many pennies would ana have in total after 10 days?

show and use the formula to calculate

show all work

 

pls help i struggle.. thank you

 May 1, 2019
 #1
avatar+104652 
+2

It's not possible to generate a geometric series from the fist one because we have no common difference....

 

But....if she were to  start with one penny and successively double the amount added the previous day.....we would have this series :

 

1,2,4,8....etc....

 

So....on the 10th day.....she would have this much :

 

1 [ 1 - 2^10 ]  / [ 1 - 2 ]  =

 

1 [- 1023] /  -1    =

 

1023 cents  =  $10.23

 

 

cool cool cool

 May 1, 2019
 #2
avatar+74 
-2

The common difference is 5 right?

She adds 5 pennies to her collection everyday, making it change by 5 everyday.

doorknoob  May 1, 2019
 #3
avatar
+1

CPhill: What were you thinking of?
10th day =F + D(N - 1), F=First day, D=Common differnce, N=Number of days.
               =1 + 5*(10 - 1)
               =1 + 5*9
               =46 cents 
Days = (1, 6, 11, 16, 21, 26, 31, 36, 41, 46)- cents

 May 1, 2019
 #4
avatar+895 
+1

But that would be an arithmetic sequence.

 

Arithmetic formula: \(t_n=t_1+(n-1)d\)

tn=nth term, t1= first term, d= common difference, n= terms

 

Geometric Formula: \(t_n=t_1*r^{(n-1)}\)

tn=nth term, t1= first term, r= common ratio, n= terms.

AdamTaurus  May 1, 2019
 #5
avatar+104652 
0

Sorry.....I meant "common ratio" instead of " common difference"

 

 

cool cool cool

 May 3, 2019

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