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Sequences and Series

Problems

General Sequences and Series

Arithmetic Sequences

Problem : Find an explicit formula for the following sequence: 1, 3, 5, 7, 9,....

a n = 2n - 1

Problem : Find three explicit formulas for the following sequence: -1, 1, -1, 1, -1, 1,… (Hint: Use trigonometric functions, too).

a n = (- 1)n ; a n = sin( + ) ; a n = cos() .

Problem : What is the 11 th term of the sequence a n = 2n - 6 ?

a 11 = 2(11) - 6 = 16 .

Problem : Calculate (4i - 5) .

(4i - 5) = - 1 + 3 + 7 + 11 + 15 + 19 = 54 .

Problem : Calculate 5(k + 2) .

5(k + 2) = 5(k + 2) = 5[6 + 7 + 8 + 9] = 150 .

Problem : Let a n = 4n 2 . What is the sum of the first five terms of a ?

(4i 2) = 4 i 2 = 4[1 + 4 + 9 + 16 + 25] = 220 .

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