You finally get an allowance! You put $2. away in January, $4. away in February, $8. away in March, $16 away in April and followed this savings pattern through to December. How much money do you have in 12 months?
I see a geometric progression here
a=2
R=2
N=12
T12=2(2)^11=?
Or,
just continue grind out the pattern, you are already at April, just a few more
and you will get Isaac's answer.
n = the number of months.
Amount = 2^n * 2 = 2^3 * 2 = $16 after the 3rd month(March).
Amount = 2^12 * 2 = $8,192.
To find out how much money you have in 12 months, you need to calculate the sum of the amounts you put away each month.
The savings pattern mentioned in the question is that you double the amount each month. So, starting with $2 in January, you have $2 in February ($2 x 2), $4 in March ($4 x 2), $8 in April ($8 x 2), and so on.
To calculate the amount you have in December, you can use the formula for geometric series, which is:
Sum = first term * (1 - common ratio ^ number of terms) / (1 - common ratio)
Here, the first term is $2, the common ratio is 2 (doubling each month), and the number of terms is 12 (12 months).
Applying the formula:
Sum = $2 * (1 - 2^12) / (1 - 2)
= $2 * (1 - 4096) / (-1)
= $2 * (-4095) / (-1)
= $8,190
Therefore, after 12 months, you would have $8,190 saved.