SOLUTION: Could someone help to solve this question: Dad wanted his car to be clean and shiny every day for a week to impress a customer of his. To hose and wipe down the car, he offered

Question 514917: Could someone help to solve this question:
Dad wanted his car to be clean and shiny every day for a week to impress a customer of his. To hose and wipe down the car, he offered to pay his son James 15 cents the first day and double the daily payment each succeeding day thereafter. If James accepted the deal, how much money did he make?

$9.60 $12.40 $14.40 $16.20 $19.05 $38.25
Thank you for your help.
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
First Day .....15
Second Day.....30
Third Day .....60
Fouth Day.....120
Fifth Day.....240
Sixth Day.....480
Seventh Day ..960
Sum..........1905
He made 1905 cents or 1905/100=19.05=$19.05
In this question there are only 7 terms invloved but if we have to calculate sum of large number of terms, we use arithematic or geometric sequences method.
We have
15,30,60,................
This is a geometric sequence in which common ratio between two consecutive terms is same.
Formula to sumup this kind of series is
Sn=a(1-r^2)/(1-r)
Where
Sn=sum of the series/sequence
a= first term
n= Total number of terms we are summing up.
r=common ratio
Common ration between two consecutive terms = 30/15 = 2
or 60/30=2 and so on.
r=2
a=15
n=7
Put above value in the formula
Sn=15(1-2^7)/(1-2)
=15(1-128)/-1
=5(-127)/-1
=-1905/-1
=1905
He made 1905 cents or 1905/100=19.05=$19.05

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