Sequences and Series Practice Problems.pdf - Math 169...

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Math 169 Sequences and Series Supplemental Linear Growth and Arithmetic Sequence Suppose that you earn $30 each day. If you start out with $100 in your savings, and you add the $30 to your savings every evening, how much will you have saved after 11 days? . 1
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Examples 1) 4, 9, 14, 19, … d = 5 2) 12, 2, -8, - 18,… d = -10 The 20 th term of the sequence is 12 + 19 (-10) = -178 The general term of the arithmetic sequence a, a + d, a + 2d, a + 3d, … is 1 n t a n d Examples 1) Determine the 30 th term of the arithmetic sequen ce 4, 7, 10, … t 30 = 4 + 29 (3) = 91 2) Find the n th term of the sequence 7, 2, -3, - 8,… t n = 7 + ( n 1)(-5) = 12 5 n The Sum of an Arithmetic Series For the general arithmetic series a + ( a + d ) + ( a + 2 d ) + …+ t n , the sum of the first n terms is: 2 n n n S a t or 2 1 2 n n S a n d Examples 1. Determine the sum of the first 30 terms of the arithmetic series 5 + 5.3 + 5.6 +…
Math 169

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