SOLUTION: kawther saved 3 nicles today if she triples the number of niclkles she saves evry day how many days including today will it take her to save more than 700 nickles

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Question 1188981: kawther saved 3 nicles today if she triples the number of niclkles she saves evry day how many days including today will it take her to save more than 700 nickles
Found 3 solutions by math_tutor2020, MathTherapy, greenestamps:
Answer by math_tutor2020(3817) About Me  (Show Source):
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Day 1 = 3 nickels
Day 2 = 9 nickels
Day 3 = 27 nickels
Day 4 = 81 nickels
Each new day, we triple the previous day's amount. Example: 9*3 = 27 when jumping from day 2 to day 3.

Let n be a positive whole number (1,2,3,...)
For day n, we have 3^n nickels.
Examples:
Day n = 2 has 3^n = 3^2 = 9 nickels
Day n = 4 has 3^n = 3^4 = 81 nickels

As you probably can notice, the sequence 3,9,27,81,... is a geometric sequence. The first term is a = 3 and the common ratio is r = 3.

Use this formula to sum the first n terms of a geometric sequence
S%5Bn%5D+=+a%2A%281-r%5En%29%2F%281-r%29

For example, let's sum the first 4 days worth of nickels.
S%5Bn%5D+=+a%2A%281-r%5En%29%2F%281-r%29

S%5B4%5D+=+3%2A%281-3%5E4%29%2F%281-3%29

S%5B4%5D+=+120
Then confirm it by adding the first four items mentioned at the top of this page: 3+9+27+81 = 120
This example helps show the S%5Bn%5D formula works. I encourage you to try other values of n.

The goal is to somehow get S%5Bn%5D to be more than 700.
We can try n = 5
S%5Bn%5D+=+a%2A%281-r%5En%29%2F%281-r%29

S%5B5%5D+=+3%2A%281-3%5E5%29%2F%281-3%29

S%5B5%5D+=+363
which unfortunately doesn't work. If you tried n = 6, then you should find that S%5B6%5D+=+1092 which fits the goal. I'll leave those steps for you.

Sure enough,
Day 1 = 3 nickels
Day 2 = 9 nickels
Day 3 = 27 nickels
Day 4 = 81 nickels
Day 5 = 243 nickels
Day 6 = 729 nickels
3+9+27+81+243+729 = 1092
which confirms S%5B6%5D+=+1092 is correct

Answer: 6 days

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

kawther saved 3 nicles today if she triples the number of niclkles she saves evry day how many days including today will it take her to save more than 700 nickles
          Sum of G.P.: matrix%281%2C3%2C+a%5B1%5D%28%28r%5En+-+1%29%2F%28r+-+1%29%29%2C+%22=%22%2C+S%5Bn%5D%29

In THIS case, we have: 

                                  

                                   You can do the check!

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The formula for the sum of a finite number of terms of a geometric series is something you should know and be able to use.

However, for a problem like this, with a small number of terms and "nice" numbers, the fastest path to the solution is to find the terms of the sequence and add them until you reach the goal.
     day  # today  total #
   ------------------------
      1      3      3
      2      9     12
      3     27     39
      4     81    120
      5    243    363
      6    729   1092

The first day when the total is greater than 700 is day 6.

ANSWER: 6