Sample Test Find the first four terms of the given sequence and state if it is arithmetic, geometric or neither.

1)  t_n = 4 ^. (-2)ⁿ 2)  t_n = 5n - 1 3)  t_n = n² + 3

Find a formula for each sequence.

4)  5, 1, -3, -7, -11, . . . 5)  -3, -6, -12, -24, -48, . . .

Find the third, fourth and fifth terms of each sequence.

6)  t₁ = 5, t₂ = 8, t_n = t_n-1 + t_n-2 7)  t₁ = 3, t_n = 2t_n-1 + n

_{Give a recursive definition for the following sequence:}

_{8)  2, 5, 11, 20, 32, 47, . . .}

For each series, find the specified sum.

9)  arithmetic,  t_n = 2 + 3n,        S₃₅ = 10)  2 + 20 + 200 + 2000 + 20000 + . . .            S₇ =

Evaluate each of the following limits, or state that it does not exist.

11)  12)  13) 

Find the sum of the given infinite series.

14)  1 + 1/4 + 1/16 + 1/64 + 1/256 + . . . 15)  2 + 4 + 8 + 16 + . . .

Find the interval of convergence and the sum expressed using x.

16)  1 + x + x² + x³ + . . .

Write the following repeating decimal as an infinite series and find the sum.

17)  .3737373737. . .

Express each series using sigma notation.

18)  1/4 + 4/9 + 9/16 + 16/25 + 25/36 + 36/49 =

Write the following series in expanded form.

19) 

Use mathematical induction to prove the following

20) 

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Hope you did well on the sample test.  Answers will be posted 3 days before the actual exam.  Next chapter covered is chapter 19.  See you then!
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