SOLUTION: I wish to save 4 dollars week one. Week 2 I wish to save the original 4 dollars plus an additional 4 dollars. Week 3 sum of week 2 plus four dollars etc for 52 weeks. How do I expr

Algebra ->  Finance -> SOLUTION: I wish to save 4 dollars week one. Week 2 I wish to save the original 4 dollars plus an additional 4 dollars. Week 3 sum of week 2 plus four dollars etc for 52 weeks. How do I expr      Log On


   

Question 842594: I wish to save 4 dollars week one. Week 2 I wish to save the original 4 dollars plus an additional 4 dollars. Week 3 sum of week 2 plus four dollars etc for 52 weeks. How do I express that algebraically?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The savings for any particular week is
$4 times the number of that week
Let +n+ = the week number.
+4n+ is the savings for week +n+
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You are letting +n+ go from +1+ to +52+
So, the expression for total savings looks like:
4*( 1 + 2 + 3 + 4 + 5 + . . . )
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The formula for the sum of all integers from
1 to n is +%28+n%2A%28+n%2B1+%29%29%2F2+
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Let +S+ = total savings for +n+ weeks
+S+=+%28+4n%2A%28+n%2B1+%29+%29%2F2+
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Now let +n+=+52+
+S+=+%28+4%2A52%2A53+%29%2F2+
+S+=+11024%2F2+
+S+=+5512+
The savings for 52 weeks is $5,512