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# Pre-Cal 20S January 20, 2009

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Building a function library & more on arithmetic sequences.

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### Pre-Cal 20S January 20, 2009

1. 1. Building a Library of Functions in the library by ﬂickr user svenwerk
2. 2. Find the next three terms in each sequence of numbers ... in the library by ﬂickr user svenwerk 4, 7, 10, 13, , , 3, 6, 12, 24, , , 32, 16, 8, 4, , , 1, 1, 2, 3, 5, 8,13, , ,
3. 3. 4, 7, 10, 13, , ,
4. 4. Some Deﬁnitions Sequence: An ordered list of numbers that follow a certain pattern (or rule). Arithmetic Sequence: (i) Recursive Deﬁnition: An ordered list of numbers generated by continuously adding a value (the common difference) to a given ﬁrst term. (ii) Implicit Deﬁnition: An ordered list of numbers where each number in the list is generated by the equation of a line. Common Difference (d): (i) The number that is repeatedly added to successive terms in an arithmetic sequence. (ii) From the implicit deﬁnition, d is the slope of the linear equation.
5. 5. To Find The Common Difference d is the common difference d = tn - t(n - 1) tn is an arbitrary term in the sequence t(n - 1) is the term immediately before tn in the sequence To Find the nth Term In an Arithmetic Sequence tn is the nth term tn = a + (n - 1)d a is the ﬁrst term n is the quot;rankquot; of the nth term in the sequence d is the common difference Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ... Implicitly? Solution: a = 11 t = 11 + (51 - 1)(-6) 51 d = 5 - 11 t51 = 11 + (50)(-6) = -6 t51 = 11 - 300 n = 51 t51 = -289