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# Pre-Cal 20S January 22, 2009

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Arithmetic series.

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### Pre-Cal 20S January 22, 2009

1. 1. The Story of Young Gauss ... really this time ... Photo Source: Karl Gauss (1777–1855)
2. 2. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the ﬁrst 5 terms. denotes the sum of the ﬁrst n terms. Artithmetic Series: The sum of numbers in an arithmetic sequence given by is the sum to the nth term n is the quot;rankquot; of the nth term a is the ﬁrst term in the sequence d is the common difference
3. 3. Find the sum of the ﬁrst 6 terms of each series: 5 + 8 + 11 + ...
4. 4. Find the sum of the ﬁrst 6 terms of each series: -6 - 8 - 10 - ...
5. 5. Find the sum of the ﬁrst 60 terms of each series: 5 + 8 + 11 + ... -6 - 8 - 10 - ...
6. 6. Find the sum of the arithmetic series ... 5 + 9 + 13 + ... + 201 -8 - 5 - 2 + ... + 139
7. 7. Find the number of terms in each of the following arithmetic sequences. -2, -8, -14, ..., -206 x + 2, x + 9, x + 16, ... , x + 303
8. 8. Complete each arithmetic sequence by ﬁnding the missing arithmetic means. 1, ____, 25 14, ____, ____, 32
9. 9. Complete each arithmetic sequence by ﬁnding the missing arithmetic means. -1.5, ____, ____, ____, 4.5 -3, ____, ____, -60
10. 10. What is the domain and range of each relation? (f) y 4 2 x -3
11. 11. Identify all the intercepts for each relation? (f) y 4 2 x -3
12. 12. Complete each arithmetic sequence by ﬁnding the missing arithmetic means. 2, ____, ____, ____, ____, 107 m + 40, ____, ____, ____, m + 4