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I = interest P = principal r = rate t = time Simple Interest and Sequences Future Value of investment: S = P + I Ex. 1: $800 is invested for 5 years at an annual rate of 14%. How much interest is earned? What is future value?

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Simple Interest (continued) Ex. 2: If you borrow $1600 for 2 years at an annual rate of 14% simple interest, how much must you pay back? How much interest is owed? What do you pay back? Ex. 3: $800 is invested at an annual rate of 14%. How much is earned in 5 months? How long does it take your investment to be worth $2200?

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A list of numbers following a certain pattern a 1, a 2, a 3, a 4, …, a n, … Pattern is determined by position or by what has come before Sequences 3, 6, 12, 24, 48, …

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Defined by n (its position) Find the first four terms and the 100 th term for the following: Partial Sums Adding the first n terms of a sequence, the n th partial sum:

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Find the first 4 partial sums and then the n th partial sum for the sequence defined by: Example 2

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Consider the following sequences: Arithmetic Sequences 4, 7, 10, 13, 16, … 81, 75, 69, 63, 57, … An arithmetic sequence is defined as: with a as the first term and d as the common difference.

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Examples

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Partial Sums Find the 1000 th partial sum for arithmetic sequence with a=1, d=1:

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Partial Sums Find the 7 th partial sum for arithmetic sequence with a=10, d=7:

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Example For the month of February, you get $4 on the first day, $7 on the second day, $10 on the third day and so on. How much will you have received in total at the end of the month?

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