SOLUTION: to save for the coming holiday season, you decided to save constantly increasing amounts of money. On the first week of your saving period, you decide to save 50 pesos and then fo

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Question 1090863: to save for the coming holiday season, you decided to save constantly increasing amounts of money. On the first week of your saving period,
you decide to save 50 pesos and then for the next week you will save 40 pesos more than what you saved in the previous week. How much money will you have after saving money for 24 weeks?
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Because there is a constant pattern in how much you save each week, there is an easy way to get the answer without adding all the 24 amounts.

You save 50 the first week, and then increase the amount by 40 each week for 24 weeks. To see how to get the answer easily, let's think about the amounts saved only in the first couple of weeks and in the last couple of weeks.

The amount saved the first week is 50; the amount saved the second week is 90.

The amount saved the last week is the original 50, plus the additional 40 added 23 times, for a total of 50+920 = 970. And so the amount saved the previous week is 970-40 = 930.

The average of the amounts for the first and last weeks is

The average of the amounts for the second and next-to-last weeks is

You might be able to see by those two calculations that the average of each such pair is going to be the same number, 510. But that means the average of ALL the amounts is 510.

And so the total amount saved in the 24 weeks is just that average of 510 multiplied by the number of weeks:

In general, any time you have a sequence of numbers like this, where there is a common difference between the numbers, the total can be calculated as

(average of first and last numbers) times (number of numbers)