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 saving pattern through to December. How much money do you have in 12 months? Please explain
Google "geometric series" or "sum of geometric series"
here r = 2
and your first value a = 2
and you do it 12 times
For example
http://www.purplemath.com/modules/series5.htm
360
To find out how much money you have in 12 months, we need to determine the total amount saved each month and then add them up.
In this case, the saving pattern is doubling the amount saved each month. We start with $2 in January and double the amount saved each subsequent month.
Here is the saving pattern:
January: $2
February: $2 * 2 = $4
March: $4 * 2 = $8
April: $8 * 2 = $16
We can continue this pattern for the remaining months:
May: $16 * 2 = $32
June: $32 * 2 = $64
July: $64 * 2 = $128
August: $128 * 2 = $256
September: $256 * 2 = $512
October: $512 * 2 = $1024
November: $1024 * 2 = $2048
December: $2048 * 2 = $4096
So, the total amount saved over 12 months is the sum of all these amounts:
$2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 + $1024 + $2048 + $4096 = $8190
Therefore, you will have a total of $8190 saved after 12 months following this saving pattern.