SOLUTION: Heather is collecting dimes. She saves one dime on the first day, two dimes on the second day and three dimes on the third day. If this pattern continues, how much money will she h

Question 825401: Heather is collecting dimes. She saves one dime on the first day, two dimes on the second day and three dimes on the third day. If this pattern continues, how much money will she have saved at the end of 30 days?
What algebraic formula would I use for this?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First we will figure out how many dimes Heather has after the 30 days. Then we will turn that number of dimes into the amount of money it is worth.

The number of dimes are:
1 after the first day
2 more after the second day
3 more after the third day
etc.
In a mathematical expression (if "x" is the number of dimes):
x = 1 + 2 + 3 + ... + 30

How many dimes is this? We could actually add up all these numbers. But it is faster if you recognize that the numbers are an arithmetic sequence. And the sum of an arithmetic sequence has a formula:

where
is the sum of the first n terms
"a" is the first term
"n" is the number of terms
"d" is the common difference
(Note: There are other variations to this formula. You may have been taught one of these. If so, just go ahead and use it. It will work out the same as this one.)
With our first term of 1, 30 terms and a common difference of 1 (1 and 2 are 1 apart, 2 and 3 are 1 apart, etc.), this becomes:

Simplifying...

So after 30 days Heather has 585 dimes! Since each dime is 1/10 of a dollar, she has 585/10 dollars which is equal to 58.5 dollars or $58.50.
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