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So I'm trying to find out the formula by writing out the expanded version first and simplifying it, but I'm not sure how to write this in terms of exponents.A deposit of $$25 is made at the beginning of the 1st month, and successive monthly deposits after that is $25 more than the previous month (2nd month is a $50 deposit, 3rd month is a $75, etc.). At the beginning of the next year (after 12 months), the deposit cycle is reset back to $25 the first month, etc. and this pattern continues for 5 years. The account pays 5% compounded interest monthly at the end of each month. What is the balance of the account after 5 years?

Month 1: [tex]25 + 25(.05)[/tex]

Let x = [tex]25 + 25(.05)[/tex]

Month 2: [tex](x + 50)(.05) + (x + 50)[/tex]

Month 3: [tex]((x + 50)(.05) + (x + 50) + 75)(.05) + ((x + 50)(.05) + (x + 50) + 75)[/tex]

Month 4: (((x + 50)(.05) + (x + 50) + 100)(.05) + ((x + 50)(.05) + (x + 50) + 100))(.05) + ((x + 50)(.05) + (x + 50) + 100)(.05) + ((x + 50)(.05) + (x + 50) + 100)

But then I remembered the formula will probably change after 12 months since the deposits start over, but the balance is different...so I'm not sure how else to really approach this.

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