Meehan98
  • Meehan98
Help with Geometric Sequences and Series, please! David gave 10 cents to his daughter on her first birthday. He decided to give her triple the amount on each subsequent birthday. How much money would his daughter have received over a period of 10 years?
Mathematics
chestercat
  • chestercat
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Meehan98
  • Meehan98
The formula is: \[a _{n}= a _{1} r ^{n-r}\]
Meehan98
  • Meehan98
I keep getting $1968.30, but that's not right. The correct choices are: $2952.40 $51.10 $102.30 $984.10
zepdrix
  • zepdrix
Your solution that you came up with should be correct. Hmm thinking...

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zepdrix
  • zepdrix
oh oh oh. No
zepdrix
  • zepdrix
On the `tenth birthday` he gave her 1968.30, you are correct. But that is not the `sum` that he gave her over the period of all those birthdays.
Meehan98
  • Meehan98
I have a sample problem that has the solution as well if that will help you.
Meehan98
  • Meehan98
I have a sample problem that has the solution as well if that will help you.
zepdrix
  • zepdrix
So this problem really is asking this:\[\large\rm \sum_{n=1}^{10} a_1 r^{n-1}\]They want you to add up all that money.
zepdrix
  • zepdrix
Partial sum of a geometric series... mmm im trying to remember the formula >.< hehe
zepdrix
  • zepdrix
\[\large\rm \sum_{n=1}^{10} a_1 r^{n-1}=a_1\left(\frac{1-r^n}{1-r}\right)\]Does that formula look familiar? :)
Meehan98
  • Meehan98
I know the formula; I didn't think about the sum! Thank you!
zepdrix
  • zepdrix
If you only have ONE OPTION over 1968.30, that should help you narrow down your sum quite a bit ;) lol
Meehan98
  • Meehan98
Yes, so the sum would be: $2,952.40!
zepdrix
  • zepdrix
yayyy good job \c:/

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