Question 1131465: George decide to put aside some money each day so he could buy a new television. He saved $1 on the first day, $1.50 on the 2nd day, $2 on the 3rd day, and so on, each day saving 50 cents more than he did the day before. He did this for 62 days. How much money George after 62 days?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The first day amount is $1; the second day amount is $1.50;...; the 62nd day amount is $1, plus 50 cents 61 times: $1+61($.50) = $31.50.
So we need to find the sum
1.00 + 1.50 + 2.00 + ... + 31.00 + 31.50
This is a sum of 62 numbers, first number 1.00 and last number 31.50, with a common difference of 0.50 between successive numbers.
Because of the common difference between the numbers, we can use a shortcut to find the answer. The sum of any set of numbers is the number of numbers, multiplied by the average of all the numbers; when there is a common difference between numbers in the set, the average of all the numbers is just the average of the first and last.
So our sum is 62 times the average of $1.00 and $31.50:
ANSWER: George saves $1007.50 in 62 days.
|
|
|
