A deposit of $100,000 is made to an investment fund at the beginning of a year. On the last day of each year two dividends are awarded. The first dividend is 20% of the amount in the account during that year. The second dividend is 45% of the amount in the account in the previous year.   Find a recurrence relation for {Pn}, where Pn is the amount in the account at the end of n years if no money is ever withdrawn.  How much is in the account after n years if no money has been withdrawn?

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.