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Problems

Problems

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

an = 2n - 1

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

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

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

a11 = 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 an = 4n2. What is the sum of the first five terms of a?

(4i2) = 4i2 = 4[1 + 4 + 9 + 16 + 25] = 220.