SOLUTION: Heather is collecting dimes. She saves 1 dime on the 1st day, 2 dimes on the 2nd day & 3 dimes on the third day. If this pattern continues, how much money will Heather have saved a

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Heather is collecting dimes. She saves 1 dime on the 1st day, 2 dimes on the 2nd day & 3 dimes on the third day. If this pattern continues, how much money will Heather have saved a      Log On

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Question 1006532: Heather is collecting dimes. She saves 1 dime on the 1st day, 2 dimes on the 2nd day & 3 dimes on the third day. If this pattern continues, how much money will Heather have saved at the end of 30 days?
* Please write in Algebric form, so I can apply the same method to other problems similar to this one. I really appreciate your help. Thanks!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have:
Sum = 10*( 1 + 2 + 3 + 4 + . . . 30 )
There's a formula for this sequence:
Sum( 1 through n ) = +%28+n%2A%28+n%2B1+%29%29%2F2+
Testing for +n+=+6+,
+1+%2B+2+%2B+3+%2B+4+%2B+5+%2B+6+=+21+
+%28+6%2A7%29%2F2+=+42%2F2+
+42%2F2+=+21+
OK
With +n+=+30+
sum = +10%2A%28%28%28+30%2A31+%29+%2F+2+%29%29+
sum = +10%2A%28+930%2F2+%29+
sum = +10%2A465+=+4650+ cents
$46.50 after 30 days